Concept:

Resistivity

• The resistivity of any substance can be defined as the electrical resistance of a conductor of a unit cross-sectional area and a unit length.
• Some have high resistivity and some have low resistivity.
• The more the resistivity, the less the amount of current carrying capacity by the material and the lesser the resistivity more is the current carrying capacity of the material.
• Higher resistivity substances are insulators and lower resistivity materials are conductors.

Explanation:

• Metals are generally considered good conductors.
• They allow current to flow through them easily because of the free electrons present in their outer shell.
• We convert metals into alloys by adding some other metals and/or nonmetals to get better properties. Most of the time non-metals are added.
• The resistivity of the alloy is greater than the resistivity of the constituent metals.
• So, R_alloy > R_A; R_alloy > R_B

CONCEPT:

Resistivity (ρ):

• The property of a conductor that opposes the flow of electric current through them and independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.
  • The unit for resistivity is the ohm-meter (Ω-m).
  • The resistivity of a material depends on its nature and the temperature of the conductor.
  • The resistivity of a material depends on its shape and size (length and area).
  • The resistivity of the conductor increases as the temperature increases.

EXPLANATION:

• The resistivity of any material depends on the temperature as

⇒ ρ_t = ρ0 [1 + α (T - T0)]

where, ρ0 = resistivity at standard temperature, ρ_t = resistivity at temperature t0 C, T0 = reference temperature, α  = the temperature coefficient of resistivity.

• The resistivity of a material depends on its shape and size (length and area).
• The resistivity of the conductor increases as the temperature increases.
• So by the above explanation, we can say that only statement 1 is correct.
• Hence, option 1 is correct.

Important Points

Resistance is given as

l is the length of the conductor, A is cross-sectional area.

It does not mean, resistivity depends on the resistance.

Resistance depends upon resistivity, but the opposite is not true.

The Correct answer is Both (A) and (C)

CONCEPT:

• Density: The mass per unit volume is called density. It is denoted by ρ.
• The density of ice is less than that of water.

Density (ρ) = Mass (M)/Volume (V)

EXPLANATION:

• Since the density of ice is less than that of water that's why it floats on the water.

• Mass (M) = ρ × V

• Consider two cases, in the first case an ice cube of mass m floating in the water, if it is floating (in equilibrium), it will have to displace enough water to support its weight. 
• Sinking of solid wax is an anomaly: This statement correctly identifies that the sinking of solid wax in liquid wax is an anomaly. In most cases, solid wax is less dense than liquid wax, and it should float on the surface. However, if the solid wax is denser than the liquid wax, it may sink instead of floating.
• The density of solid wax is less than liquid wax: This statement is incorrect. The sinking of solid wax in liquid wax suggests that the density of the solid wax might be higher than that of the liquid wax. Solid objects generally float in a liquid if their density is less than the density of the liquid.

The correct answer is 2 only.

Key Points.

Water movement in a dropper:

• Water moves from higher pressure to lower pressure.
• Water rises in the dropper due to atmospheric pressure. Hence 2 is correct.
• When the bulb is pressed, the air is present in the tube, and the bulb escapes in the form of bubbles.
• Due to this, Pressure inside the bulb decreases, however, there is atmospheric pressure on the surface of the liquid.
• When we release the bulb, the water moves inside the tube.

Additional Information

Atmospheric pressure:

• Atmospheric pressure also called barometric pressure, is force per unit area exerted by an atmospheric column (that is, the entire body of air above the specified area).
• Atmospheric pressure can be measured with a mercury barometer (hence the commonly used synonym barometric pressure), which indicates the height of a column of mercury that exactly balances the weight of the column of the atmosphere over the barometer.

CONCEPT:

• Projectile motion: An object that is in flight after being thrown or projected is called a projectile.
• The motion of the projectile can be seen as the combination of two  separate simultaneous motions:​    

1. a velocity component in the horizontal direction without acceleration.
2. a velocity component in the vertical direction with constant acceleration due to the force of gravity.

• Maximum height of the projectile (H_m): Maximum verticle height, above the point of projection, attained by the projectile during its flight.

• Where v₀ is the velocity with which the projectile is thrown, θ is the angle of projection with the x-axis, and g is the acceleration due to gravity. 
• Horizontal range (R): The horizontal distance covered by the projectile between its initial position (x = y = 0) and the final position (y = 0).

CALCULATION:

Given that:

Hence option 1) is correct.

Additional Information

Equation of path of a projectile: 

where v0 is the velocity with which the projectile is thrown, θ is the angle of projection with the x-axis, x is the horizontal displacement of the projectile, and g is the acceleration due to gravity.

Concept:

Velocity - time graph:

• The velocity-time graph is a plot between Velocity and Time.
• It shows the Motion of the object that moves in a Straight Line.
• The magnitude of Velocity at a given instant is equal to its Instantaneous Speed.
• The distance traveled by an object can be calculated from the area under a velocity-time graph.
• The area under the graph can be calculated by: using geometry (if the lines are straight) and counting the squares beneath the line (particularly if the lines are curved).

Calculation:

We know that 1 min = 60s

The total distance traveled by bus can be calculated as,

S = area of a triangle + area of a rectangle

S = (0.5 × length × height) + (length × width)

S = (0.5 × 60 × 10 × 60) + (60 × 10 × 60)

S = 54000 m

S = 54 km

Hence, the total distance traveled by bus is 54 km.

Explanation:

Statement 1

• This statement is incorrect. The microphone does not convert sound directly to a mechanical signal.
• It typically uses a transducer (such as a condenser or a dynamic element) that converts sound waves into an electrical signal.

Statement 2

• This statement is correct. The primary function of a microphone is to convert sound waves into an electrical signal.
• This electrical signal can then be processed and transmitted through various electronic devices.

Statement 3

• This statement is incorrect. The speaker does not convert a mechanical signal to sound. Instead, it converts an electrical signal into sound waves.
• The electrical signal passes through the speaker's voice coil, which interacts with a magnet, causing the speaker cone to vibrate and produce sound.

Statement 4

• This statement is correct. The speaker converts an electrical signal into sound.
• It receives the electrical signal from the audio source (such as a mobile phone), and through the interaction of the voice coil and the magnet, it generates sound waves that can be heard by the listener.

The correct statements are:

The microphone converts sound to an electrical signal.

The speaker converts an electrical signal to sound.

The correct answer is option (4)

Explanation:

→ At the poles of the earth, the angle of dip is 90^o.

∴ the Components of earth's magnetic field(B_E) at the poles are:

→ Vertical component V = B_Esin(90^o)

V = B_E

→ Horizontal component H = B_Ecos(90^o)

H = 0

→ Thus a magnetic needle free to rotate will orient vertically along the poles of the earth as the horizontal component of the earth's magnetic field is zero.

Hence, the correct option is (1).

Concept:

Energy conservation Principal:

Rotational Energy + Kinetic Energy = Potential Energy

Calculation:

Given:

The sphere is rolling on a frictionless surface  To find = Translational velocity  (V) to clime the inclined surface.

Now,

Energy conservation Principal:

Rotational Energy + Kinetic Energy =Potential Energy

Explanation:

Electromagnetic: It is defined as when an electric current is flowing through a conductor it will show some magnetic property and this magnetic behavior is known as electromagnetic.

Diamagnetic material - It is defined as when the magnetic field is applied to the material, it will be aligned in the direction of the magnetic field and when we remove the magnetic field it will regain its original position which is in the opposite direction of the magnetic field.

⇒ When a thin diamagnetic rod is placed between the poles of an electromagnet it will experience a magnetic force on the material when the current will pass on it.

⇒ Due to this magnetic force, the rod will be pushed up and out of the horizontal magnetic field, and in resulting the rod gains gravitational potential energy due to the work done by the electric current in the diamagnetic rod. 

⇒ Therefore we can say that the energy of the current source will be converted into the potential energy of the rod.

Hence, option 1) is the correct answer.