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 adiabatic elasticity of a gas is equal to

1. $\gamma \times$density                               

2. $\gamma \times$volume

3. $\gamma \times$pressure                             

4. $\gamma \times$specific heat

The specific heat at constant pressure and at constant volume for an ideal gas are $C_p$ and $C_v$ and its adiabatic and isothermal elasticities are $E_{\varnothing }$ and$E_{\theta }$  respectively. The  ratio of $E_{\varnothing }$ to $E_{\theta }$ is

1. $C_v/C_p$

2. $C_p/C_v$

3. $C_p{C}_v$

4. $1/C_p{C}_v$

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. \(0.4~\text{cc}\)
2. \(4\times 10^{-5}~\text{cc}\)
3. \(0.025~\text{cc}\)
4. \(0.004~\text{cc}\)

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:

A ball falling into a lake of depth \(200~\text{m}\) shows a \(0.1\%\) decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?
1. \(19.6\times 10^{8}~\text{N/m}^2\)
2. \(19.6\times 10^{-10}~\text{N/m}^2\)
3. \(19.6\times 10^{10}~\text{N/m}^2\)
4. \(19.6\times 10^{-8}~\text{N/m}^2\)

The Bulk modulus for an incompressible liquid is:

1. Zero                                           

2. Unity

3. Infinity                                       

4. Between 0 to 1

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

1. $3\times {10}^{12}N/m^2$                       

2. $2\times {10}^{12}N/m^2$

3. ${10}^{12}N/m^2$                           

4. None of the above