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 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. $1/C_p{C}_v$

If the volume of the given mass of a gas is increased four times and the temperature is raised from 27°C to 127°C. The isothermal elasticity will become

1. 4 times                               

2. 1/4 times

3. 3 times                               

4. 1/3 times

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. $19.6\times {10}^{-8}N/m^2$