The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.6 mm ?

(Young’s modulus for brass = $0.9\times {10}^{11}N/m^2$)

A 5 m long aluminium wire $\left(Y=7\times {10}^{10}N/m^2\right)$ of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in a copper wire $\left(Y=12\times {10}^{10}N/m^2\right)$ of the same length under the same weight, the diameter of the copper wire should be, in mm:

A steel wire of 1 m long and  cross section area $1 {\mathrm{mm}}^2$ is hang from rigid end. When mass of 1kg is hung from it then change in length will be: (given $Y=2\times {10}^{11}N/m^2$)

An iron rod of length 2m and cross section area of 50 X ${10}^{-6} m^2$ , is stretched by 0.5 mm, when a mass of 250 kg is hung from its lower end. Young's modulus of the iron rod is-

In which case, there is a maximum extension in the wire, if the same force is applied on each wire?

The extension of a wire by the application of load is 3 mm. The extension in a wire of the same material and length but half the radius by the same load is -

The isothermal elasticity of a gas is equal to

The adiabatic elasticity of a gas is equal to

(a) $\gamma \times$density                                (b) $\gamma \times$volume

(c) $\gamma \times$pressure                              (d) $\gamma \times$specific heat

The compressibility of water is $4\times {10}^{-5}$ per unit atmospheric pressure. The decrease in volume of 100 cubic centimeter of water under a pressure of 100 atmosphere will be -

If a rubber ball is taken at the depth of 200 m in a pool, its volume decreases by 0.1%. If the density of the water is $1\times {10}^{3}kg/m^3$ and $g=10m/s^2$, then the volume elasticity in  will be

When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces by 0.01%. The bulk modulus of the material of the rubber in $dyne / c{m}^2$ is:

A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is

A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball

The Bulk modulus for an incompressible liquid is

The ratio of lengths of two rods A and B of the same material is 1: 2 and the ratio of their radii is 2: 1. The ratio of modulus of rigidity of A and B will be:

When a spiral spring is stretched by suspending a load on it, the strain produced is called:

The Young's modulus of the material of a wire is $6\times {10}^{12}N/m^2$ and  there is no transverse strain in it, then its modulus of rigidity will be

Modulus of rigidity of a liquid:

A cube of aluminium of sides 0.1 m is subjected to a shearing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

A rod of length l and radius r is joined to a rod of length l/2 and radius r/2 of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of $\theta$, the twist angle at the joint will be 

Shearing stress causes a change in-

To break a wire, a force of ${10}^{6}N/m^2$ is required. If the density of the material is $3\times {10}^3 kg/m^3$, then the length of the wire which will break by its own weight will be -

The strain-stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that
           

The diagram shows a force-extension graph for a rubber band. Consider the following statements

I. It will be easier to compress this rubber than expand it

II. Rubber does not return to its original length after it is stretched

III. The rubber band will get heated if it is stretched and released

 Which of these can be deduced from the graph?

The adjacent graph shows the extension $\left(∆l\right)$ of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross sectional area of the wire is ${10}^{-6}{m}^2$ calculate the young’s modulus of the material of the wire

The graph shows the behaviour of a length of wire in the region for which the substance obeys Hook’s law. P and Q represent

The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that

If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be

Two wires of same diameter of the same material having the length l and 2l. If the force F is applied on each, the ratio of the work done in the two wires will be