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:

1. 1.75                                  
2. 1.5
3. 2.5                                   
4. 5.0

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

1. 0.5 mm                             

2. 0.25 mm

3. 0.05 mm                           

4. 5 mm

An iron rod of length 2m and cross section area of 50 X ${10}^{-6}<mspace\; width="1em"></mspace>m^2$ , 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-

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

2. $19.6\times {10}^{15}N/m^2$

3. $19.6\times {10}^{18}N/m^2$                         

4. $19.6\times {10}^{20}N/m^2$

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

1. L = 500 cm, d = 0.05 mm

2. L = 200 cm, d = 0.02 mm

3. L = 300 cm, d = 0.03 mm

4. L = 400 cm, d = 0.01 mm

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