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A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is
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Initial speed of ball is zero and it finally attains terminal speed
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason (R): A coil spring of copper has more tensile strength than a steel spring of same dimensions.
In the light of the above statements, choose the most appropriate answer from the options given below
It is true that stretching of spring is determined by shear modulus of the spring as when coil spring is stretched neither its length nor its volume changes, there is only change in its shape.
Tensile strength of steel is more than that of copper.
Hence Assertion is true and reason is false.
A The terminal velocity of a copper ball of radius 5mm falling through a tank of oil at room temperature is 10cms−1. If the viscosity of oil at room temperature is 0.9kgm−1s−1, the viscous drag force is:
Given, r = 5mm = 5 × 10−3m Vt = 10cms−1 = 10 × 10−2m−1s
Viscous drag force
F = 6πηrVt
F = 6 × π × 0.9 × 5 × 10−3 × 10 × 10−2
F = 84.78 × 10−4
F = 8.478 × 10−3N
The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be
I. Let Fv be the viscous force and FB be the Bouyant force acting on the ball.
A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :
Force of surface tension balances the weight of water in capillary tube.
FS = 2πrT cosθ = mg
Here, T and θ are constant.
So, m ∝ r
Let m1 and m2 be the mass of water in two capillary tube.
A small hole of area of cross-section 2mm2 is present near the bottom of a fully filled open tank of height 2m. Taking g = 10m/s2, the rate of flow of water through the open hole would be nearly
A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 × 10−2N/m.
The pressure inside the bubble equals at a point Z0 below the free surface of water in a container. Taking g = 10m/s2, density of water = 103kg/m3, the value of Z0 is
The stress-strain curves are drawn for two different materials X and Y. It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y. We can say that materials X and Y are likely to be (respectively)
Fracture point and ultimate strength point is close for material X, hence X is brittle in nature and both points are far apart for material Y hence it is ductile.
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by ∆l on applying a force F, how much force is needed to stretch the second wire by the same amount?
Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2 The thermal conductivity of the composite rod will be
Equivalent thermal conductivity of the composite rod in parallel combination will be,
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