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 -

1. 12 mm                                 

2. 0.75 mm

3. 15 mm

4. 6 mm

The isothermal elasticity of a gas is equal to

1. Density                                     

2. Volume

3. Pressure                                    

4. Specific heat

The adiabatic elasticity of a gas is equal to
1. γ × density
2. γ × volume
3. γ × pressure
4. γ × 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 -

1. 0.4 cc         
2. $4\times {10}^{-5}cc$
3. 0.025 cc     
4. 0.004 cc 

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

1. ${10}^8$                                       

2. $2\times {10}^8$

3. ${10}^9$                                         

4. $2\times {10}^9$

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:

1. $10\times {10}^{12}$                               

2. $100\times {10}^{12}$

3. $1\times {10}^{12}$                                 

4. $20\times {10}^{12}$

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

1. 0.01                             

2. 0.06

3. 0.02                             

4. 0.03

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

1. $19.6\times {10}^{8}N/m^2$               

2. $19.6\times {10}^{-10}N/m^2$

3. $19.6\times {10}^{10}N/m^2$               

4. $19.6\times {10}^{-8}N/m^2$

The Bulk modulus for an incompressible liquid is

1. Zero                                           

2. Unity

3. Infinity                                       

4. Between 0 to 1

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: