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)   1.75                                   (b)   1.5

(c)   2.5                                     (d)   5.0

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 $Y=2\times {10}^{11}N/m^2$)

(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 ${10}^{-6} m^2$ , 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 -

(a) 0.4 cc           (b) $4\times {10}^{-5}cc$

(c) 0.025 cc       (d) 0.004 cc