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Solution
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Q.1 Correct
Q.1 In-correct
Q.1 Unattempt

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $\mathrm{M} \sqrt{\frac{\mathrm{GMR}}{x}}$. The value of $x$ is _________ , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)



JEE Main 2025 (Online) 23rd January Evening Shift

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $\mathrm{M} \sqrt{\frac{\mathrm{GMR}}{x}}$. The value of $x$ is _________ , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)



JEE Main 2025 (Online) 23rd January Evening Shift
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

Acceleration due to gravity on the surface of earth is ' $g$ '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________ g.



JEE Main 2025 (Online) 24th January Evening Shift

Acceleration due to gravity on the surface of earth is ' $g$ '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________ g.



JEE Main 2025 (Online) 24th January Evening Shift
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt

Two planets, $A$ and $B$ are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B=2 R_A$. The planet $B$ is $4 \sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{\mathrm{L}_{\mathrm{B}}}{\mathrm{L}_{\mathrm{A}}}\right)$ of angular momentum $\left(L_B\right)$ of planet $B$ to that of planet $A\left(L_A\right)$ is closest to integer ________.



JEE Main 2025 (Online) 29th January Evening Shift

Two planets, $A$ and $B$ are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B=2 R_A$. The planet $B$ is $4 \sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{\mathrm{L}_{\mathrm{B}}}{\mathrm{L}_{\mathrm{A}}}\right)$ of angular momentum $\left(L_B\right)$ of planet $B$ to that of planet $A\left(L_A\right)$ is closest to integer ________.



JEE Main 2025 (Online) 29th January Evening Shift
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is____________ $\times 10^{10} \mathrm{~J}$.

(Mass of earth $=6 \times 10^{24} \mathrm{~kg}$, Radius of earth $=6.4 \times 10^6 \mathrm{~m}$, Gravitational constant $=6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$ )



JEE Main 2025 (Online) 2nd April Evening Shift

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is____________ $\times 10^{10} \mathrm{~J}$.

(Mass of earth $=6 \times 10^{24} \mathrm{~kg}$, Radius of earth $=6.4 \times 10^6 \mathrm{~m}$, Gravitational constant $=6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$ )



JEE Main 2025 (Online) 2nd April Evening Shift
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length $a$. When released, they interact only through gravitational force and collide after a time $\mathrm{T}=4$ seconds. If the sides of the triangle are increased to length $2 a$ and also the masses of the spheres are made 2 m , then they will collide after__________seconds.

JEE Main 2025 (Online) 3rd April Morning Shift
Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length $a$. When released, they interact only through gravitational force and collide after a time $\mathrm{T}=4$ seconds. If the sides of the triangle are increased to length $2 a$ and also the masses of the spheres are made 2 m , then they will collide after__________seconds.

JEE Main 2025 (Online) 3rd April Morning Shift
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt

A small point of mass $m$ is placed at a distance $2 R$ from the centre ' $O$ ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is $\mathrm{F}_1$. A spherical part of radius $\mathrm{R} / 3$ is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of $M$ is found to be $F_2$. The value of ratio $F_1: F_2$ is

JEE Main 2025 (Online) 22nd January Morning Shift Physics - Gravitation Question 12 English



JEE Main 2025 (Online) 22nd January Morning Shift

A small point of mass $m$ is placed at a distance $2 R$ from the centre ' $O$ ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is $\mathrm{F}_1$. A spherical part of radius $\mathrm{R} / 3$ is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of $M$ is found to be $F_2$. The value of ratio $F_1: F_2$ is

JEE Main 2025 (Online) 22nd January Morning Shift Physics - Gravitation Question 12 English



JEE Main 2025 (Online) 22nd January Morning Shift
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $=27$ days and gravitational attraction between the satellite and the moon is neglected.



JEE Main 2025 (Online) 23rd January Evening Shift

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $=27$ days and gravitational attraction between the satellite and the moon is neglected.



JEE Main 2025 (Online) 23rd January Evening Shift
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by

JEE Main 2025 (Online) 24th January Morning Shift
A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by

JEE Main 2025 (Online) 24th January Morning Shift
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:



JEE Main 2025 (Online) 28th January Evening Shift

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:



JEE Main 2025 (Online) 28th January Evening Shift
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt

Match the LIST-I with LIST-II 

Choose the correct answer from the options given below:

Match the LIST-I with LIST-II 

Choose the correct answer from the options given below:
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A : The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2} \mathrm{mgR}$, where R is the radius of earth.

Reason R : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.

In the light of the above statements, choose the correct answer from the options given below



JEE Main 2025 (Online) 4th April Morning Shift

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A : The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2} \mathrm{mgR}$, where R is the radius of earth.

Reason R : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.

In the light of the above statements, choose the correct answer from the options given below



JEE Main 2025 (Online) 4th April Morning Shift
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt

An object is kept at rest at a distance of $3 R$ above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :(Assume $\mathrm{M}=$ mass of earth, $\mathrm{G}=$ Universal gravitational constant)



JEE Main 2025 (Online) 4th April Evening Shift

An object is kept at rest at a distance of $3 R$ above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :(Assume $\mathrm{M}=$ mass of earth, $\mathrm{G}=$ Universal gravitational constant)



JEE Main 2025 (Online) 4th April Evening Shift
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.

Reason (R): For a central force field the angular momentum is a constant.

In the light of the above statements, choose the most appropriate answer from the options given below:



JEE Main 2025 (Online) 7th April Evening Shift

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.

Reason (R): For a central force field the angular momentum is a constant.

In the light of the above statements, choose the most appropriate answer from the options given below:



JEE Main 2025 (Online) 7th April Evening Shift
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

[27-Jan-2024 Shift 1]

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

[27-Jan-2024 Shift 1]
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt

At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as R.)

[29-Jan-2024 Shift 1]

At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as R.)

[29-Jan-2024 Shift 1]
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?

[29-Jan-2024 Shift 2]

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?

[29-Jan-2024 Shift 2]
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt

The gravitational potential at a point above the surface of earth is −5.12 × 107J∕kg and the acceleration due to gravity at that point is 6.4m∕ s2. Assume that the mean radius of earth to be 6400km. The height of this point above the earth's surface is :

[30-Jan-2024 Shift 1]

The gravitational potential at a point above the surface of earth is −5.12 × 107J∕kg and the acceleration due to gravity at that point is 6.4m∕ s2. Assume that the mean radius of earth to be 6400km. The height of this point above the earth's surface is :

[30-Jan-2024 Shift 1]
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt

Escape velocity of a body from earth is 11.2km∕ s. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

[30-Jan-2024 Shift 2]

Escape velocity of a body from earth is 11.2km∕ s. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

[30-Jan-2024 Shift 2]
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt

Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is  the length of the sides of the square is

[31-Jan-2024 Shift 1]

Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is  the length of the sides of the square is

[31-Jan-2024 Shift 1]
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt

The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

[31-Jan-2024 Shift 2]

The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

[31-Jan-2024 Shift 2]
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g = π2m∕ s2, then the length of the second's pendulum at a height h = 2R from the surface of earth will be,:

[1-Feb-2024 Shift 1]

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g = π2m∕ s2, then the length of the second's pendulum at a height h = 2R from the surface of earth will be,:

[1-Feb-2024 Shift 1]
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt

A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T. If the force of attraction between planet and star is proportional to R −3∕2 then choose the correct option :

[1-Feb-2024 Shift 2]

A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T. If the force of attraction between planet and star is proportional to R −3∕2 then choose the correct option :

[1-Feb-2024 Shift 2]
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
Assertion A: A pendulum clock when taken to Mount Everest becomes fast.
Reason R: The value of g (acceleration due to gravity) is less at MountEverest than its value on the surface of earth.
In the light of the above statements, choose the most appropriate answer from the options given below
[24-Jan-2023 Shift 2]
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
Assertion A: A pendulum clock when taken to Mount Everest becomes fast.
Reason R: The value of g (acceleration due to gravity) is less at MountEverest than its value on the surface of earth.
In the light of the above statements, choose the most appropriate answer from the options given below
[24-Jan-2023 Shift 2]
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth Re=6400‌km )
[24-Jan-2023 Shift 1]
The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth Re=6400‌km )
[24-Jan-2023 Shift 1]
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
Given below are two statements:
Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II: Acceleration due to earth's gravity is same at a height ' h ' and depth ' d ' from earth's surface, if h=d.
In the light of above statements, choose the most appropriate answer form the options given below
[24-Jan-2023 Shift 2]
Given below are two statements:
Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II: Acceleration due to earth's gravity is same at a height ' h ' and depth ' d ' from earth's surface, if h=d.
In the light of above statements, choose the most appropriate answer form the options given below
[24-Jan-2023 Shift 2]
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
If the distance of the earth from Sun is 1.5×106 km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:
[24-Jan-2023 Shift 2]
If the distance of the earth from Sun is 1.5×106 km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:
[24-Jan-2023 Shift 2]
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100g. The time period of the motion of the particle will be (approximately)
(take g=10ms−2,radius of earth =6400‌km )
[25-Jan-2023 Shift 1]
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100g. The time period of the motion of the particle will be (approximately)
(take g=10ms−2,radius of earth =6400‌km )
[25-Jan-2023 Shift 1]
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be:
[25-Jan-2023 Shift 1]
T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be:
[25-Jan-2023 Shift 1]
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
A body of mass is taken from earth surface to the height h equal to twice the radius of earth (Re), the increase in potential energy will be : ( g= acceleration due to gravity on the surface of Earth)
[25-Jan-2023 Shift 2]
A body of mass is taken from earth surface to the height h equal to twice the radius of earth (Re), the increase in potential energy will be : ( g= acceleration due to gravity on the surface of Earth)
[25-Jan-2023 Shift 2]
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
Every planet revolves around the sun in an elliptical orbit :
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun
C. The centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.
Choose the correct answer from the options given below :
Options :
[25-Jan-2023 Shift 2]
Every planet revolves around the sun in an elliptical orbit :
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun
C. The centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.
Choose the correct answer from the options given below :
Options :
[25-Jan-2023 Shift 2]
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
Two particles of equal mass ' m ' move in a circle of radius ' r ' under the action of their mutual gravitational attraction. The speed of each particle will be :
[29-Jan-2023 Shift 1]
Two particles of equal mass ' m ' move in a circle of radius ' r ' under the action of their mutual gravitational attraction. The speed of each particle will be :
[29-Jan-2023 Shift 1]
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.
[29-Jan-2023 Shift 2]
The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.
[29-Jan-2023 Shift 2]
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
If the gravitational field in the space is given as (−‌
K
r2
). Taking the reference point to be at r=2‌cm with gravitational potential V=10J∕kg. Find the gravitational potential at r=3‌cm in SI unit (Given, that K=6J‌cm∕kg )
[30-Jan-2023 Shift 1]
If the gravitational field in the space is given as (−‌
K
r2
). Taking the reference point to be at r=2‌cm with gravitational potential V=10J∕kg. Find the gravitational potential at r=3‌cm in SI unit (Given, that K=6J‌cm∕kg )
[30-Jan-2023 Shift 1]
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
At a certain depth "d" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface. Where R is Radius of earth (Take R=6400‌km ). The depth d is equal to
[31-Jan-2023 Shift 1]
At a certain depth "d" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface. Where R is Radius of earth (Take R=6400‌km ). The depth d is equal to
[31-Jan-2023 Shift 1]
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following \{Assume negligible air friction\}
[31-Jan-2023 Shift 1]
Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following \{Assume negligible air friction\}
[31-Jan-2023 Shift 1]
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:
[31-Jan-2023 Shift 2]
A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:
[31-Jan-2023 Shift 2]
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
Given below are two statements :
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer from the options given below
[1-Feb-2023 Shift 1]
Given below are two statements :
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer from the options given below
[1-Feb-2023 Shift 1]
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
If earth has a mass nine times and radius twice to the of a planet P. Then ‌
ve
3
√xms−1 will be the minimum velocity required by a rocket to pull out of gravitational force of P, where ve is escape velocity on earth. The value of x is
[1-Feb-2023 Shift 1]
If earth has a mass nine times and radius twice to the of a planet P. Then ‌
ve
3
√xms−1 will be the minimum velocity required by a rocket to pull out of gravitational force of P, where ve is escape velocity on earth. The value of x is
[1-Feb-2023 Shift 1]
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
For a body projected at an angle with the horizontal from the ground, choose the correct statement.
[1-Feb-2023 Shift 2]
For a body projected at an angle with the horizontal from the ground, choose the correct statement.
[1-Feb-2023 Shift 2]
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
The escape velocities of two planets A and B are in the ratio 1:2. If the ratio of their radii respectively is 1:3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be:
[1-Feb-2023 Shift 2]
The escape velocities of two planets A and B are in the ratio 1:2. If the ratio of their radii respectively is 1:3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be:
[1-Feb-2023 Shift 2]
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:
[6-Apr-2023 shift 1]
A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:
[6-Apr-2023 shift 1]
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Earth has atmosphere whereas moon doesn't have any atmosphere.
Reason R : The escape velocity on moon is very small as compared to that on earth.
In the light of the above statements. choose the correct answer from the options given below:
[6-Apr-2023 shift 1]
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Earth has atmosphere whereas moon doesn't have any atmosphere.
Reason R : The escape velocity on moon is very small as compared to that on earth.
In the light of the above statements. choose the correct answer from the options given below:
[6-Apr-2023 shift 1]
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
The weight of a body on the surface of the earth is 100N. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is :
[6-Apr-2023 shift 2]
The weight of a body on the surface of the earth is 100N. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is :
[6-Apr-2023 shift 2]
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
Choose the incorrect statement from the following :
[6-Apr-2023 shift 2]
Choose the incorrect statement from the following :
[6-Apr-2023 shift 2]
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
Given below are two statements:
Statement I : If E be the total energy of a satellite moving around the earth, then its potential energy will be ‌
E
2

Statement II : The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy E.
In the light of the above statements, choose the most appropriate answer from the options given below
[8-Apr-2023 shift 1]
Given below are two statements:
Statement I : If E be the total energy of a satellite moving around the earth, then its potential energy will be ‌
E
2

Statement II : The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy E.
In the light of the above statements, choose the most appropriate answer from the options given below
[8-Apr-2023 shift 1]
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
The weight of a body on the earth is 400N. Then weight of the body when taken to a depth half of the radius of the earth will be:
[8-Apr-2023 shift 1]
The weight of a body on the earth is 400N. Then weight of the body when taken to a depth half of the radius of the earth will be:
[8-Apr-2023 shift 1]
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth center is increased by eight times to its initial value, then the new angular momentum will be-
[8-Apr-2023 shift 2]
The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth center is increased by eight times to its initial value, then the new angular momentum will be-
[8-Apr-2023 shift 2]
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
The acceleration due to gravity at height h above the earth if h<<R (Radius of earth) is given by
[8-Apr-2023 shift 2]
The acceleration due to gravity at height h above the earth if h<<R (Radius of earth) is given by
[8-Apr-2023 shift 2]
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r&3r respectively. The ratio of orbital speeds of the satellites respectively is
[10-Apr-2023 shift 1]
Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r&3r respectively. The ratio of orbital speeds of the satellites respectively is
[10-Apr-2023 shift 1]
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=‌
R
2
 from the surface of earth, if its weight on the surface of earth is 200N, will be :
[10-Apr-2023 shift 1]
Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=‌
R
2
 from the surface of earth, if its weight on the surface of earth is 200N, will be :
[10-Apr-2023 shift 1]
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If the earth suddenly shrinks to ‌
1
64
 th of its original volume with its mass remaining the same, the period of rotation of earth becomes ‌
24
x
h. The value of x is _______.
[10-Apr-2023 shift 1]
If the earth suddenly shrinks to ‌
1
64
 th of its original volume with its mass remaining the same, the period of rotation of earth becomes ‌
24
x
h. The value of x is _______.
[10-Apr-2023 shift 1]
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
Given below are two statements:
Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g)
Statement II : The effect of rotation of the earth on the value of ' g ' at the equator is minimum and that at the pole is maximum.
In the light of the above statements, choose the correct answer from the options given below.
[10-Apr-2023 shift 2]
Given below are two statements:
Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g)
Statement II : The effect of rotation of the earth on the value of ' g ' at the equator is minimum and that at the pole is maximum.
In the light of the above statements, choose the correct answer from the options given below.
[10-Apr-2023 shift 2]
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given g=π2m∕ s2,R= radius of earth)
[10-Apr-2023 shift 2]
The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given g=π2m∕ s2,R= radius of earth)
[10-Apr-2023 shift 2]
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are ρ and ρ∕3 respectively. The ratio of acceleration due to gravity at their surfaces (gA:gB) will be :
[11-Apr-2023 shift 1]
The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are ρ and ρ∕3 respectively. The ratio of acceleration due to gravity at their surfaces (gA:gB) will be :
[11-Apr-2023 shift 1]
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
A space ship of mass 2×104‌kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g=10m∕ s2 and radius of earth =6400‌km ):
[11-Apr-2023 shift 2]
A space ship of mass 2×104‌kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g=10m∕ s2 and radius of earth =6400‌km ):
[11-Apr-2023 shift 2]
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be
[12-Apr-2023 shift 1]
Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be
[12-Apr-2023 shift 1]
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
The ratio of escape velocity of a planet to the escape velocity of earth will be :-
Given : Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.
[12-Apr-2023 shift 1]
The ratio of escape velocity of a planet to the escape velocity of earth will be :-
Given : Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.
[12-Apr-2023 shift 1]
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
A planet having mass 9‌Me and radius 4‌Re, where Me and Re are mass and radius of earth respectively, has escape velocity in km∕ s given by:
(Given escape velocity on earth Ve=11.2×103m∕ s )
[13-Apr-2023 shift 1]
A planet having mass 9‌Me and radius 4‌Re, where Me and Re are mass and radius of earth respectively, has escape velocity in km∕ s given by:
(Given escape velocity on earth Ve=11.2×103m∕ s )
[13-Apr-2023 shift 1]
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
Two planets A and B of radii R and 1.5R have densities ρ and ρ∕2 respectively. The ratio of acceleration due to gravity at the surface of B to A is :
[13-Apr-2023 shift 2]
Two planets A and B of radii R and 1.5R have densities ρ and ρ∕2 respectively. The ratio of acceleration due to gravity at the surface of B to A is :
[13-Apr-2023 shift 2]
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
Given below are two statements :
Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement II : Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer form the options given below
[13-Apr-2023 shift 2]
Given below are two statements :
Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement II : Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer form the options given below
[13-Apr-2023 shift 2]
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
The approximate height from the surface of earth at which the weight of the body becomes ‌
1
3
 of its weight on the surface of earth is :
[Radius of earth R=6400‌km and √3=1.732 ]
[24-Jun-2022-Shift-1]
The approximate height from the surface of earth at which the weight of the body becomes ‌
1
3
 of its weight on the surface of earth is :
[Radius of earth R=6400‌km and √3=1.732 ]
[24-Jun-2022-Shift-1]
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be:
[24-Jun-2022-Shift-2]
The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be:
[24-Jun-2022-Shift-2]
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be: (Given g= acceleration due to gravity at the surface of earth).
[25-Jun-2022-Shift-1]
The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be: (Given g= acceleration due to gravity at the surface of earth).
[25-Jun-2022-Shift-1]
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
Two satellites S1 and S2 are revolving in circular orbits around a planet with radius R1=3200‌km and R2=800‌km respectively. The ratio of speed of satellite S1 to be speed of satellite S2 in their respective orbits would be ‌
1
x
 where x=
[25-Jun-2022-Shift-2]
Two satellites S1 and S2 are revolving in circular orbits around a planet with radius R1=3200‌km and R2=800‌km respectively. The ratio of speed of satellite S1 to be speed of satellite S2 in their respective orbits would be ‌
1
x
 where x=
[25-Jun-2022-Shift-2]
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
The variation of acceleration due to gravity (g) with distance ( r) from the center of the earth is correctly represented by :
(Given R= radius of earth)
[26-Jun-2022-Shift-1]
The variation of acceleration due to gravity (g) with distance ( r) from the center of the earth is correctly represented by :
(Given R= radius of earth)
[26-Jun-2022-Shift-1]
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
The elongation of a wire on the surface of the earth is 10−4m. The same wire of same dimensions is elongated by 6×10−5m on another planet. The acceleration due to gravity on the planet will be ___ ms−2. (Take acceleration due to gravity on the surface of earth =10ms−2 )
[26-Jun-2022-Shift-1]
The elongation of a wire on the surface of the earth is 10−4m. The same wire of same dimensions is elongated by 6×10−5m on another planet. The acceleration due to gravity on the planet will be ___ ms−2. (Take acceleration due to gravity on the surface of earth =10ms−2 )
[26-Jun-2022-Shift-1]
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below:
[26-Jun-2022-Shift-2]
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below:
[26-Jun-2022-Shift-2]
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
Two identical particles each of mass ' m ' go round a circle of radius a under the action of their mutual gravitational attraction. The angular speed of each particle will be :
[15-Apr-2023 shift 1]
Two identical particles each of mass ' m ' go round a circle of radius a under the action of their mutual gravitational attraction. The angular speed of each particle will be :
[15-Apr-2023 shift 1]
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
Given below are two statements :
Statement I: The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below.
[27-Jun-2022-Shift-1]
Given below are two statements :
Statement I: The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below.
[27-Jun-2022-Shift-1]
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
Four spheres each of mass m from a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is :

[27-Jun-2022-Shift-2]
Four spheres each of mass m from a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is :

[27-Jun-2022-Shift-2]
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA=2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?
[28-Jun-2022-Shift-1]
Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA=2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?
[28-Jun-2022-Shift-1]
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
Water falls from a 40m high dam at the rate of 9×104‌kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100W lamps, that can be lit, is :
(. Take .g=10ms−2)
[28-Jun-2022-Shift-2]
Water falls from a 40m high dam at the rate of 9×104‌kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100W lamps, that can be lit, is :
(. Take .g=10ms−2)
[28-Jun-2022-Shift-2]
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be :
[28-Jun-2022-Shift-2]
Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be :
[28-Jun-2022-Shift-2]
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
The escape velocity of a body on a planet ' A ' is 12kms−1. The escape velocity of the body on another planet ' B ', whose density is four times and radius is half of the planet ' A ', is :
[29-Jun-2022-Shift-1]
The escape velocity of a body on a planet ' A ' is 12kms−1. The escape velocity of the body on another planet ' B ', whose density is four times and radius is half of the planet ' A ', is :
[29-Jun-2022-Shift-1]
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be
[29-Jun-2022-Shift-2]
The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be
[29-Jun-2022-Shift-2]
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
Three identical particles A,B and C of mass 100kg each are placed in a straight line with AB=BC=13m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately:
[25-Jul-2022-Shift-1]
Three identical particles A,B and C of mass 100kg each are placed in a straight line with AB=BC=13m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately:
[25-Jul-2022-Shift-1]
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
An object is taken to a height above the surface of earth at a distance ‌
5
4
R from the centre of the earth. Where radius of earth, R=6400km. The percentage decrease in the weight of the object will be
[25-Jul-2022-Shift-2]
An object is taken to a height above the surface of earth at a distance ‌
5
4
R from the centre of the earth. Where radius of earth, R=6400km. The percentage decrease in the weight of the object will be
[25-Jul-2022-Shift-2]
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
The percentage decrease in the weight of a rocket, when taken to a height of 32‌km above the surface of earth will, be :
( Radius of earth =6400‌km )
[26-Jul-2022-Shift-1]
The percentage decrease in the weight of a rocket, when taken to a height of 32‌km above the surface of earth will, be :
( Radius of earth =6400‌km )
[26-Jul-2022-Shift-1]
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be :
(Take radius of earth =6400‌km and g=10ms−2 )
[26-Jul-2022-Shift-2]
A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be :
(Take radius of earth =6400‌km and g=10ms−2 )
[26-Jul-2022-Shift-2]
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
Two satellites A and B, having masses in the ratio 4:3, are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is :
[27-Jul-2022-Shift-1]
Two satellites A and B, having masses in the ratio 4:3, are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is :
[27-Jul-2022-Shift-1]
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
A body of mass m is projected with velocity λve in vertically upward direction from the surface of the earth into space. It is given that ve is escape velocity and λ<1. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be :
( R : radius of earth)
[27-Jul-2022-Shift-2]
A body of mass m is projected with velocity λve in vertically upward direction from the surface of the earth into space. It is given that ve is escape velocity and λ<1. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be :
( R : radius of earth)
[27-Jul-2022-Shift-2]
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :
[28-Jul-2022-Shift-1]
If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :
[28-Jul-2022-Shift-1]
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
Assume there are two identical simple pendulum clocks. Clock −1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6s respectively. Then the value of h is___
(consider radius of earth RE=6400‌km and g on earth 10m∕ s2 )
[28-Jul-2022-Shift-2]
Assume there are two identical simple pendulum clocks. Clock −1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6s respectively. Then the value of h is___
(consider radius of earth RE=6400‌km and g on earth 10m∕ s2 )
[28-Jul-2022-Shift-2]
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth αh(h<<Re) from the earth surface. The value of α will be ________.
‌ (use ‌Re=6400‌km‌ ) ‌
[29-Jul-2022-Shift-1]
If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth αh(h<<Re) from the earth surface. The value of α will be ________.
‌ (use ‌Re=6400‌km‌ ) ‌
[29-Jul-2022-Shift-1]
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
An object of mass 1‌kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g=10ms−2 and radius of earth =6400‌km]
[29-Jul-2022-Shift-2]
An object of mass 1‌kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g=10ms−2 and radius of earth =6400‌km]
[29-Jul-2022-Shift-2]
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
A cylindrical wire of radius 0.5mm and conductivity 5×107S∕m is subjected to an electric field of 10mV∕m. The expected value of current in the wire will be x3πmA. The value of x is .......... .
[24 Feb 2021 Shift 2]
A cylindrical wire of radius 0.5mm and conductivity 5×107S∕m is subjected to an electric field of 10mV∕m. The expected value of current in the wire will be x3πmA. The value of x is .......... .
[24 Feb 2021 Shift 2]
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now, a spherical cavity of radius (‌
R
2
) is made in the sphere (as shown in figure) and the force becomes F2. The value of F1:F2 is

[25 Feb 2021 Shift 1]
A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now, a spherical cavity of radius (‌
R
2
) is made in the sphere (as shown in figure) and the force becomes F2. The value of F1:F2 is

[25 Feb 2021 Shift 1]
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
A planet revolving in elliptical orbit has
I. a constant velocity of revolution
II. has the least velocity when it is nearest to the Sun
III. its areal velocity is directly proportional to its velocity
IV. areal velocity is inversely proportional to its velocity.
V. to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below.
[26 Feb 2021 Shift 1]
A planet revolving in elliptical orbit has
I. a constant velocity of revolution
II. has the least velocity when it is nearest to the Sun
III. its areal velocity is directly proportional to its velocity
IV. areal velocity is inversely proportional to its velocity.
V. to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below.
[26 Feb 2021 Shift 1]
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
A body weights 49N on a spring balance at the North pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator ? (Use, g=‌
GM
R2
=9.8ms−2 and radius of earth, R=6400km )
[24 Feb 2021 Shift 2]
A body weights 49N on a spring balance at the North pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator ? (Use, g=‌
GM
R2
=9.8ms−2 and radius of earth, R=6400km )
[24 Feb 2021 Shift 2]
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
Find the gravitational force of attraction between the ring and sphere as shown in the figure, where the plane of the ring is perpendicular to the line joining the centres. If √8R is the distance between the centres of a ring (of mass m ) and a sphere (of mass M ), where both have equal radius R.

[26 Feb 2021 Shift 1]
Find the gravitational force of attraction between the ring and sphere as shown in the figure, where the plane of the ring is perpendicular to the line joining the centres. If √8R is the distance between the centres of a ring (of mass m ) and a sphere (of mass M ), where both have equal radius R.

[26 Feb 2021 Shift 1]
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
A person standing on a spring balance inside a stationary lift measures 60kg. The weight of that person, if the lift descends with uniform downward acceleration of 1.8m∕s2 will be ........... N. [g=10m∕s2]
[26 Feb 2021 Shift 1]
A person standing on a spring balance inside a stationary lift measures 60kg. The weight of that person, if the lift descends with uniform downward acceleration of 1.8m∕s2 will be ........... N. [g=10m∕s2]
[26 Feb 2021 Shift 1]
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
In the reported figure of Earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the Earth). The value of OA:AB will be x:y. The value of x is .......... .

[26 Feb 2021 Shift 2]
In the reported figure of Earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the Earth). The value of OA:AB will be x:y. The value of x is .......... .

[26 Feb 2021 Shift 2]
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
Two satellites A and B of masses 200kg and 400kg are revolving around the Earth at height of 600km and 1600km, respectively. If TA and TB are the time periods of A and B respectively, then the value of TB−TA is
(Given, radius of Earth =6400km, mass of Earth =6×1024kg )
[25 Feb 2021 Shift 1]
Two satellites A and B of masses 200kg and 400kg are revolving around the Earth at height of 600km and 1600km, respectively. If TA and TB are the time periods of A and B respectively, then the value of TB−TA is

(Given, radius of Earth =6400km, mass of Earth =6×1024kg )
[25 Feb 2021 Shift 1]
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion (A) When a rod lying freely is heated, no thermal stress is developed in it.
Reason (R) On heating, the length of the rod increases.
In the light of the above statements, choose the correct answer from the options given below
[25 Feb 2021 Shift 1]
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion (A) When a rod lying freely is heated, no thermal stress is developed in it.
Reason (R) On heating, the length of the rod increases.
In the light of the above statements, choose the correct answer from the options given below
[25 Feb 2021 Shift 1]
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
The initial velocity vi required to project a body vertically upward from the surface of the Earth to reach a height of 10R, where R is the radius of the Earth, may be described in terms of escape velocity ve such that vi=√‌
x
y
×ve. The value of x will be ........... .
[25 Feb 2021 Shift 2]
The initial velocity vi required to project a body vertically upward from the surface of the Earth to reach a height of 10R, where R is the radius of the Earth, may be described in terms of escape velocity ve such that vi=√‌
x
y
×ve. The value of x will be ........... .
[25 Feb 2021 Shift 2]
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :
[24 Feb 2021 shift 1]
Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :
[24 Feb 2021 shift 1]
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
Four identical particles of equal masses 1kg made to move along the circumference of a circle of radius 1m under the action of their own mutual gravitational attraction. The speed of each particle will be :
[24 Feb 2021 Shift 1]
Four identical particles of equal masses 1kg made to move along the circumference of a circle of radius 1m under the action of their own mutual gravitational attraction. The speed of each particle will be :
[24 Feb 2021 Shift 1]
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
Consider two satellites S1 and S2 with periods of revolution 1hr. and 8hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1 to the angular velocity of satellites S2 is
[24feb2021shift1]
Consider two satellites S1 and S2 with periods of revolution 1hr. and 8hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1 to the angular velocity of satellites S2 is
[24feb2021shift1]
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
The maximum and minimum distance of a comet from the Sun are 1.6×1012m and 8.0×1010m, respectively. If the speed of the comet at the nearest point is 6×104ms−1, then the speed at the farthest point is
[16 Mar 2021 Shift 1]
The maximum and minimum distance of a comet from the Sun are 1.6×1012m and 8.0×1010m, respectively. If the speed of the comet at the nearest point is 6×104ms−1, then the speed at the farthest point is
[16 Mar 2021 Shift 1]
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
A geostationary satellite is orbiting around an arbitrary planet P at a height of 11R above the surface of P,R being the radius of P. The time period of another satellite in hours at a height of 2R from the surface of P is P has the time period of 24h.
[17 Mar 2021 Shift 2]
A geostationary satellite is orbiting around an arbitrary planet P at a height of 11R above the surface of P,R being the radius of P. The time period of another satellite in hours at a height of 2R from the surface of P is P has the time period of 24h.
[17 Mar 2021 Shift 2]
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is
[18 Mar 2021 Shift 1]
The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is
[18 Mar 2021 Shift 1]
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
The angular momentum of a planet of mass M moving around the Sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is
[18 Mar 2021 Shift 2]
The angular momentum of a planet of mass M moving around the Sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is
[18 Mar 2021 Shift 2]
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
If the angular velocity of Earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately (Take 2g=10ms−2, the radius of Earth, R=6400×103m, take π=3.14)
[18 Mar 2021 Shift 2]
If the angular velocity of Earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately (Take 2g=10ms−2, the radius of Earth, R=6400×103m, take π=3.14)
[18 Mar 2021 Shift 2]
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is ______ S.
[22 Jul 2021 Shift 2]
A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is ______ S.
[22 Jul 2021 Shift 2]
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be ‌
x
5
‌
GM2
R
, where x is
(Round off to the nearest integer) ( M is the mass of earth, R is the radius of earth and G is the gravitational constant.)
[16 Mar 2021 Shift 2]
If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be ‌
x
5
‌
GM2
R
, where x is
(Round off to the nearest integer) ( M is the mass of earth, R is the radius of earth and G is the gravitational constant.)
[16 Mar 2021 Shift 2]
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
The radius in kilometre to which the present radius of Earth (R=6400km) to be compressed so that the escape velocity is increased 10 times is
[17 Mar 2021 Shift 1]
The radius in kilometre to which the present radius of Earth (R=6400km) to be compressed so that the escape velocity is increased 10 times is
[17 Mar 2021 Shift 1]
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
A body of mass 2M splits into four masses {m,M−m,m,M−m}, which are rearranged to form a square as shown in the figure. The ratio of
M
m
 for which, the gravitational potential energy of the system becomes maximum is x:1 . The value of x is......... .

[27 Aug 2021 Shift 1]
A body of mass 2M splits into four masses {m,M−m,m,M−m}, which are rearranged to form a square as shown in the figure. The ratio of
M
m
 for which, the gravitational potential energy of the system becomes maximum is x:1 . The value of x is......... .

[27 Aug 2021 Shift 1]
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is √
a
7
GM
R
 then the value of 'a' is ________.
[Given : The two planets are fixed in their position]

[27 Jul 2021 Shift 1]
Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is √
a
7
GM
R
 then the value of 'a' is ________.
[Given : The two planets are fixed in their position]

[27 Jul 2021 Shift 1]
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is :
[20 Jul 2021 Shift 2]
A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is :
[20 Jul 2021 Shift 2]
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0×103km. Find the mass of Mars.
{Given‌
4π2
G
=6×1011N−1m−2kg2}
[27 Jul 2021 Shift 2]
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0×103km. Find the mass of Mars.
{Given‌
4π2
G
=6×1011N−1m−2kg2}
[27 Jul 2021 Shift 2]
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A mass of 50‌kg is placed at the centre of a uniform spherical shell of mass 100‌kg and radius 50m. If the gravitational potential at a point, 25m from the centre isV‌kg∕m. The value of V is
[27 Aug 2021 Shift 2]
A mass of 50‌kg is placed at the centre of a uniform spherical shell of mass 100‌kg and radius 50m. If the gravitational potential at a point, 25m from the centre isV‌kg∕m. The value of V is
[27 Aug 2021 Shift 2]
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
If RE be the radius of Earth, then the ratio between the acceleration due to gravity at a depth r below and a height r above the Earth surface is (Given, r<RE)
[31 Aug 2021 Shift 2]
If RE be the radius of Earth, then the ratio between the acceleration due to gravity at a depth r below and a height r above the Earth surface is (Given, r<RE)
[31 Aug 2021 Shift 2]
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
Inside a uniform spherical shell
I. the gravitational field is zero.
II. the gravitational potential is zero.
III. the gravitational field is same everywhere
IV. the gravitation potential is same everywhere.
V. All of the above
Choose the most appropriate answer from the options given below.
[26 Aug 2021 Shift 1]
Inside a uniform spherical shell
I. the gravitational field is zero.
II. the gravitational potential is zero.
III. the gravitational field is same everywhere
IV. the gravitation potential is same everywhere.
V. All of the above
Choose the most appropriate answer from the options given below.
[26 Aug 2021 Shift 1]
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
The masses and radii of the Earth and Moon are (m1,R1) and (m2,R2), respectively. Their centres are at a distance r apart. Find the minimum escape velocity for a particle of mass m to be projected from the middle of these two masses.
[31 Aug 2021 Shift 1]
The masses and radii of the Earth and Moon are (m1,R1) and (m2,R2), respectively. Their centres are at a distance r apart. Find the minimum escape velocity for a particle of mass m to be projected from the middle of these two masses.
[31 Aug 2021 Shift 1]
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
Two satellites revolve around a planet in coplanar circular orbits in anti-clockwise direction. Their period of revolutions are 1h and 8h, respectively. The radius of the orbit of nearer satellite is 2×103‌km. The angular speed of thefarther satellite as observed from the nearer satellite at the instant when both the satellites are closest is
π
x
‌rad‌h−1, where x is
[1 Sep 2021 Shift 2]
Two satellites revolve around a planet in coplanar circular orbits in anti-clockwise direction. Their period of revolutions are 1h and 8h, respectively. The radius of the orbit of nearer satellite is 2×103‌km. The angular speed of thefarther satellite as observed from the nearer satellite at the instant when both the satellites are closest is
π
x
‌rad‌h−1, where x is
[1 Sep 2021 Shift 2]
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is

[1 Sep 2021 Shift 2]
Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is

[1 Sep 2021 Shift 2]
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
Consider two solid spheres of radii R1=1m,R2=2m and masses M1 and M2, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of
m1
m2
 is:

[8 Jan. 2020 I]
Consider two solid spheres of radii R1=1m,R2=2m and masses M1 and M2, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of
m1
m2
 is:

[8 Jan. 2020 I]
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s.
Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/ s)? Give your answer to the nearest integer in kilometer/s _____.
[NA 8 Jan. 2020 II]
An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s.
Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/ s)? Give your answer to the nearest integer in kilometer/s _____.
[NA 8 Jan. 2020 II]
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
A box weighs 196 N on a spring balance at the north pole.
Its weight recorded on the same balance if it is shifted to the equator is close to (Take g=10ms–2 at the north pole and the radius of the earth = 6400 km):
[7 Jan. 2020 II]
A box weighs 196 N on a spring balance at the north pole.
Its weight recorded on the same balance if it is shifted to the equator is close to (Take g=10ms–2 at the north pole and the radius of the earth = 6400 km):
[7 Jan. 2020 II]
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
A body A of mass m is moving in a circular orbit of radius Rabout a planet. Another body B of mass
m
2
 collides with A with a velocity which is half (
→
v
2
) the instantaneous velocity
→
v
 or A. The collision is completely inelastic. Then, the combined body:
[9 Jan. 2020 I]
A body A of mass m is moving in a circular orbit of radius Rabout a planet. Another body B of mass
m
2
 collides with A with a velocity which is half (
→
v
2
) the instantaneous velocity
→
v
 or A. The collision is completely inelastic. Then, the combined body:
[9 Jan. 2020 I]
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then
vA
vB
=
n
4
. The value of n is:
[9 Jan. 2020 II]
Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then
vA
vB
=
n
4
. The value of n is:
[9 Jan. 2020 II]
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R(R= radius of the earth ), it ejects a rocket of mass
m
10
 so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( G is the gravitational constant; M is the mass of the earth):
[7 Jan. 2020 I]
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R(R= radius of the earth ), it ejects a rocket of mass
m
10
 so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( G is the gravitational constant; M is the mass of the earth):
[7 Jan. 2020 I]
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
The mass density of a spherical galaxy varies as frac‌K‌r over a large distance 'r' from its centre. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:
[2 Sep. 2020 (I)]
The mass density of a spherical galaxy varies as frac‌K‌r over a large distance 'r' from its centre. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:
[2 Sep. 2020 (I)]
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become √
3
2
 times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is :
[3 Sep. 2020 (I)]
A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become √
3
2
 times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is :
[3 Sep. 2020 (I)]
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is :
[4 Sep. 2020 (II)]
A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is :
[4 Sep. 2020 (II)]
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
The value of acceleration due to gravity is g1 at a height h=
R
2
(R= radius of the earth) from the surface of the earth. It is again equal to g1 and a depth d below the sur-face of the earth. The ratio (
d
R
) equals:
[5 Sep. 2020 (I)]
The value of acceleration due to gravity is g1 at a height h=
R
2
(R= radius of the earth) from the surface of the earth. It is again equal to g1 and a depth d below the sur-face of the earth. The ratio (
d
R
) equals:
[5 Sep. 2020 (I)]
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω. An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is: (h<<R, where R is the radius of the earth)
[5 Sep. 2020 (II)]
The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω. An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is: (h<<R, where R is the radius of the earth)
[5 Sep. 2020 (II)]
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
The height 'h' at which the weight of a body will be the same as that at the same depth 'h' from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected) :
[2 Sep. 2020 (II)]
The height 'h' at which the weight of a body will be the same as that at the same depth 'h' from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected) :
[2 Sep. 2020 (II)]
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of smaller planet, the minimum firing speed needed is :
[6 Sep. 2020 (II)]
Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of smaller planet, the minimum firing speed needed is :
[6 Sep. 2020 (II)]
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by
Ax
(x2+a2)3∕2
 in the x -direction. Th magnitude of gravitational potential on the x -axis at a distance x, taking its value to be zero at infinity, is:
[4 Sep. 2020 (I)]
On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by
Ax
(x2+a2)3∕2
 in the x -direction. Th magnitude of gravitational potential on the x -axis at a distance x, taking its value to be zero at infinity, is:
[4 Sep. 2020 (I)]
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
The mass density of a planet of radius R varies with the distance r from its centre as ρ(r)=ρ0(1−
r2
R2
). Then the gravitational field is maximum at:
[3 Sep. 2020 (II)]
The mass density of a planet of radius R varies with the distance r from its centre as ρ(r)=ρ0(1−
r2
R2
). Then the gravitational field is maximum at:
[3 Sep. 2020 (II)]
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is :
[NA 6 Sep. 2020 (I)]
A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is :
[NA 6 Sep. 2020 (I)]
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is:
[9 Jan. 2019 I]
If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is:
[9 Jan. 2019 I]
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on point mass ‘m’ at x = 0,if the mass per unit length of the rod is A+Bx2 , is given by:
[12 Jan. 2019 I]
A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on point mass ‘m’ at x = 0,if the mass per unit length of the rod is A+Bx2 , is given by:
[12 Jan. 2019 I]
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
The energy required to take a satellite to a height 'h' above Earth surface (radius of Eareth =6.4×103km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal, is:
[9 Jan. 2019 II]
The energy required to take a satellite to a height 'h' above Earth surface (radius of Eareth =6.4×103km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal, is:
[9 Jan. 2019 II]
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely in elastically. The speeds of the satellite and the meteorite are the same, Just before the collision. The subsequent motion of the combined body will be
[12 Jan. 2019 I]
A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely in elastically. The speeds of the satellite and the meteorite are the same, Just before the collision. The subsequent motion of the combined body will be
[12 Jan. 2019 I]
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA∕TB, is :
[12 Jan. 2019 II]
Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA∕TB, is :
[12 Jan. 2019 II]
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
A satellite is revolving in a circular orbit at a height h from the earth surface, such that h < < R where R is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:
[11 Jan. 2019 I]
A satellite is revolving in a circular orbit at a height h from the earth surface, such that h < < R where R is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:
[11 Jan. 2019 I]
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:
[10 Jan. 2019 I]
A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:
[10 Jan. 2019 I]
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
Two stars of masses 3×1031kg each, and at distance 2×1011m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is:
(Take Gravitational constant G=66×10−11Nm2kg−2)
[10 Jan. 2019 II]
Two stars of masses 3×1031kg each, and at distance 2×1011m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is:
(Take Gravitational constant G=66×10−11Nm2kg−2)
[10 Jan. 2019 II]
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9:4. The mass of the planet is
1
9
 th of that of the Earth. If ' R ' is the radius of the Earth, what is the radius of the planet? (Take the planets to have the same mass density).
[12 April 2019 II]
The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9:4. The mass of the planet is
1
9
 th of that of the Earth. If ' R ' is the radius of the Earth, what is the radius of the planet? (Take the planets to have the same mass density).
[12 April 2019 II]
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
The value of acceleration due to gravity at Earth's surface is 9.8ms−2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9ms−2, is close to : (Radius of earth =6.4×106m )
[10 April 2019 I]
The value of acceleration due to gravity at Earth's surface is 9.8ms−2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9ms−2, is close to : (Radius of earth =6.4×106m )
[10 April 2019 I]
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance ' 3a ' from the centre will be:
[9 April 2019 I]
A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance ' 3a ' from the centre will be:
[9 April 2019 I]
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of others’ gravitational field in a circular orbit circumscribing the square ?

[8 April 2019 I]
Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of others’ gravitational field in a circular orbit circumscribing the square ?

[8 April 2019 I]
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
A test particle is moving in circular orbit in the gravitational field produced by a mass density r(r)=
K
r2
. Identify the correct relation between the radius R of the particle's orbit and its period T:
[8 April 2019 II]
A test particle is moving in circular orbit in the gravitational field produced by a mass density r(r)=
K
r2
. Identify the correct relation between the radius R of the particle's orbit and its period T:
[8 April 2019 II]
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
A spaceship orbits around a planet at a height of 20km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet ? [Given : Mass of Planet =8×1022kg, Radius of planet =2×106m, Gravitational constant G=6.67×10−11Nm2∕kg2]
[10 April 2019 II]
A spaceship orbits around a planet at a height of 20km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet ? [Given : Mass of Planet =8×1022kg, Radius of planet =2×106m, Gravitational constant G=6.67×10−11Nm2∕kg2]
[10 April 2019 II]
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth’s volume is 64 times the volume of the moon.
[8 April 2019 II]
A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth’s volume is 64 times the volume of the moon.
[8 April 2019 II]
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
Take the mean distance of the moon and the sun from the earth to be 0.4×106km and 150×106km respectively. Their masses are 8×1022kg and 2×1030kg respectively. The radius of the earth is 6400km. Let ΔF1 be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF2 be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to
ΔF1
ΔF2
 is:
[Online April 15, 2018]
Take the mean distance of the moon and the sun from the earth to be 0.4×106km and 150×106km respectively. Their masses are 8×1022kg and 2×1030kg respectively. The radius of the earth is 6400km. Let ΔF1 be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF2 be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to
ΔF1
ΔF2
 is:
[Online April 15, 2018]
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence.
[Online April 16, 2018]
Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence.
[Online April 16, 2018]
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius
R
2
, and the other mass, in a circular orbit of radius
3R
2
. The difference between the final and initial total energies is:
[Online April 15, 2018]
A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius
R
2
, and the other mass, in a circular orbit of radius
3R
2
. The difference between the final and initial total energies is:
[Online April 15, 2018]
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight
3
4
W. Radius of the Earth is 6400km and g=10m∕s2.
[Online April 8, 2017]
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight
3
4
W. Radius of the Earth is 6400km and g=10m∕s2.
[Online April 8, 2017]
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
The mass density of a spherical body is given by ρ(r)=
k
r
 for r≤R and ρ(r)=0 for r>R
where r is the distance from the centre.
The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :
[Online April 9, 2017]
The mass density of a spherical body is given by ρ(r)=
k
r
 for r≤R and ρ(r)=0 for r>R
where r is the distance from the centre.
The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :
[Online April 9, 2017]
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
Figure shows elliptical path abed of a planet around the sun S such that the area of triangle csa is
1
4
 the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semi minor axis. If t1 is the time taken for planet to go over path abs and t2 for path taken over cda then:

[Online April 9, 2016]
Figure shows elliptical path abed of a planet around the sun S such that the area of triangle csa is
1
4
 the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semi minor axis. If t1 is the time taken for planet to go over path abs and t2 for path taken over cda then:

[Online April 9, 2016]
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R;h<<R ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.)
[2016]
A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R;h<<R ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.)
[2016]
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth's surface. The radius of the earth is R, while its mass is M. The gravitational pull FG on the astronaut is :
[Online April 10, 2016]
An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth's surface. The radius of the earth is R, while its mass is M. The gravitational pull FG on the astronaut is :
[Online April 10, 2016]
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure.
Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is :
(G = gravitational constant)

[2015]
From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure.
Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is :
(G = gravitational constant)

[2015]
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
Which of the following most closely depicts the correct variation of the gravitational potential V(r) due to a large planet of radius R and uniform mass density ? (figures are not drawn to scale)
[Online April 11, 2015]
Which of the following most closely depicts the correct variation of the gravitational potential V(r) due to a large planet of radius R and uniform mass density ? (figures are not drawn to scale)
[Online April 11, 2015]
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R(R < < L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre.
If the time period of star is T and its distance from the galaxy’s axis is r, then :
[Online April 10, 2015]
A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R(R < < L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre.
If the time period of star is T and its distance from the galaxy’s axis is r, then :
[Online April 10, 2015]
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earth's orbit is ae=1.5×1011m, that of Mars orbit am= 2.28×1011m, taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to:

[Online April 9, 2014]
India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earth's orbit is ae=1.5×1011m, that of Mars orbit am= 2.28×1011m, taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to:

[Online April 9, 2014]
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is:
[2014]
Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is:
[2014]
Q.161 Correct
Q.161 In-correct
Q.161 Unattempt
From a sphere of mass M and radius R, a smaller sphere of radius
R
2
 is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is:

[Online April 11, 2014]
From a sphere of mass M and radius R, a smaller sphere of radius
R
2
 is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is:

[Online April 11, 2014]
Q.162 Correct
Q.162 In-correct
Q.162 Unattempt
The gravitational field in a region is given by
→
g
=5N∕kg
^
i
+12N∕kg
^
j
. The change in the gravitational potential energy of a particle of mass 1kg when it is taken from the origin to a point (7m,−3m) is:
[Online April 19, 2014]
The gravitational field in a region is given by
→
g
=5N∕kg
^
i
+12N∕kg
^
j
. The change in the gravitational potential energy of a particle of mass 1kg when it is taken from the origin to a point (7m,−3m) is:
[Online April 19, 2014]
Q.163 Correct
Q.163 In-correct
Q.163 Unattempt
Two hypothetical planets of masses m1 and m2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is 'd'?
(Speed of m1 is v1 and that of m2 is v2 )
[Online April 12, 2014]

Two hypothetical planets of masses m1 and m2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is 'd'?
(Speed of m1 is v1 and that of m2 is v2 )
[Online April 12, 2014]
Q.164 Correct
Q.164 In-correct
Q.164 Unattempt
The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is:
(mass of the moon =7.36×1022kg, radius of the moon's orbit =3.8×108m).
[Online April 22, 2013]
The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is:
(mass of the moon =7.36×1022kg, radius of the moon's orbit =3.8×108m).
[Online April 22, 2013]
Q.165 Correct
Q.165 In-correct
Q.165 Unattempt
The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P, located as shown, would be (nearly) :

[Online April 9, 2013]
The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P, located as shown, would be (nearly) :

[Online April 9, 2013]
Q.166 Correct
Q.166 In-correct
Q.166 Unattempt
What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?
[2013]
What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?
[2013]
Q.167 Correct
Q.167 In-correct
Q.167 Unattempt
The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius):
[Online May 7, 2012]
The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius):
[Online May 7, 2012]
Q.168 Correct
Q.168 In-correct
Q.168 Unattempt
Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of r from the centre is proportional to
[Online May 12, 2012]
Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of r from the centre is proportional to
[Online May 12, 2012]
Q.169 Correct
Q.169 In-correct
Q.169 Unattempt
The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are 10 m/s‌2 and 6400 km respectively.
The required energy for this work will be
[2012]
The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are 10 m/s‌2 and 6400 km respectively.
The required energy for this work will be
[2012]
Q.170 Correct
Q.170 In-correct
Q.170 Unattempt
A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C. When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be
[Online May 26, 2012]
A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C. When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be
[Online May 26, 2012]
Q.171 Correct
Q.171 In-correct
Q.171 Unattempt
Two particles of equal mass ‘m’ go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is
[2011 RS]
Two particles of equal mass ‘m’ go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is
[2011 RS]
Q.172 Correct
Q.172 In-correct
Q.172 Unattempt
Two bodies of masses m and 4 m are placed at a distance r.
The gravitational potential at a point on the line joining them where the gravitational field is zero is:
[2011]
Two bodies of masses m and 4 m are placed at a distance r.
The gravitational potential at a point on the line joining them where the gravitational field is zero is:
[2011]
Q.173 Correct
Q.173 In-correct
Q.173 Unattempt
The height at which the acceleration due to gravity becomes
g
9
( where g= the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is
[2009]
The height at which the acceleration due to gravity becomes
g
9
( where g= the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is
[2009]
Q.174 Correct
Q.174 In-correct
Q.174 Unattempt
This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides 4 π GM. and
Statement-2: If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ from the source is given as
1
r2
, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.
[2008]
This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides 4 π GM. and
Statement-2: If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ from the source is given as
1
r2
, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.
[2008]
Q.175 Correct
Q.175 In-correct
Q.175 Unattempt
A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s‌–1, the escape velocity from the surface of the planet would be
[2008]
A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s‌–1, the escape velocity from the surface of the planet would be
[2008]
Q.176 Correct
Q.176 In-correct
Q.176 Unattempt
The change in the value of ' g ' at a height ' h ' above the surface of the earth is the same as at a depth ' d ' below the surface of earth. When both ' d ' and ' h ' are much smaller than the radius of earth, then which one of the following is correct?
[2005]
The change in the value of ' g ' at a height ' h ' above the surface of the earth is the same as at a depth ' d ' below the surface of earth. When both ' d ' and ' h ' are much smaller than the radius of earth, then which one of the following is correct?
[2005]
Q.177 Correct
Q.177 In-correct
Q.177 Unattempt
Average density of the earth
[2005]
Average density of the earth
[2005]
Q.178 Correct
Q.178 In-correct
Q.178 Unattempt
A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere
(you may take G=6.67×10−11Nm2∕kg2)
[2005]
A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere
(you may take G=6.67×10−11Nm2∕kg2)
[2005]
Q.179 Correct
Q.179 In-correct
Q.179 Unattempt
If ‘g’ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ‘m’ raised from the surface of the earth to a height equal to the radius ‘R' of the earth is
[2004]
If ‘g’ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ‘m’ raised from the surface of the earth to a height equal to the radius ‘R' of the earth is
[2004]
Q.180 Correct
Q.180 In-correct
Q.180 Unattempt
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius ‘R’ around the sun will be proportional to
[2004]
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius ‘R’ around the sun will be proportional to
[2004]
Q.181 Correct
Q.181 In-correct
Q.181 Unattempt
The time period of an earth satellite in circular orbit is independent of
[2004]
The time period of an earth satellite in circular orbit is independent of
[2004]
Q.182 Correct
Q.182 In-correct
Q.182 Unattempt
A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
[2004]
A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
[2004]
Q.183 Correct
Q.183 In-correct
Q.183 Unattempt
The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become
[2003]
The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become
[2003]
Q.184 Correct
Q.184 In-correct
Q.184 Unattempt
Two spherical bodies of mass M and 5M & radii R & 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
[2003]
Two spherical bodies of mass M and 5M & radii R & 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
[2003]
Q.185 Correct
Q.185 In-correct
Q.185 Unattempt
The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be
[2003]
The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be
[2003]
Q.186 Correct
Q.186 In-correct
Q.186 Unattempt
Energy required to move a body of mass m from an orbit of radius 2R to 3R is
[2002]
Energy required to move a body of mass m from an orbit of radius 2R to 3R is
[2002]
Q.187 Correct
Q.187 In-correct
Q.187 Unattempt
The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is
[2002]
The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is
[2002]
Q.188 Correct
Q.188 In-correct
Q.188 Unattempt
If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will
[2002]
If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will
[2002]
Q.189 Correct
Q.189 In-correct
Q.189 Unattempt
The escape velocity of a body depends upon mass as
[2002]
The escape velocity of a body depends upon mass as
[2002]
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