A wire of diameter 1mm  breaks under a tension of 1000 N. Another wire, of the same material as that of the first one, but of diameter 2 mm, breaks under a tension of:

(1)   500 N                               

(2)   1000 N

(3)   10000 N                           

(4)   4000 N

There is no change in the volume of a wire due to change in its length on stretching. The Poisson's ratio of the material of the wire is

(1)   + 0.50                               

(2)   – 0.50

(3)   0.25                                  

(4)   – 0.25

The force required to stretch a steel wire of cross-section $1 {\mathrm{cm}}^2$ to 1.1 times its length would be $\left(Y=2\times {10}^{11} N{m}^{-2}\right)$

(1) $2\times {10}^{6}N$                               

(2) $2\times {10}^{3}N$

(3) $2\times {10}^{-6}N$                             

(4) $2\times {10}^{-7}N$

The ratio of two specific heats of gas $C_p/C_v$ for argon is 1.6 and for hydrogen is 1.4. Adiabatic elasticity of argon at pressure P is E. Adiabatic elasticity of hydrogen will also be equal to E at the pressure :

(1) P                                       

(2) $\frac{8}{7}P$

(3) $\frac{7}{8}P$                                   

(4) 1.4P

A fixed volume of iron is drawn into a wire of length L. The extension x produced in this wire by a constant force F is proportional to:

(1) $\frac{1}{L^2}$                                             

(2) $\frac{1}{L}$

(3) $L^2$                                               

(4) L

The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

(1) a - b                                             

(2) 5b - 4a

(3) 2b -$\frac{1}{4}\mathrm{a}$                                       

(4) 4a - 3b

How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.6 mm ?

(Young’s modulus for brass = $0.9\times {10}^{11}N/m^2$)

(a) Nearly 17 N                        (b) Nearly 34 N

(c) Nearly 51 N                        (d) Nearly 68 N

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) $19.6\times {10}^{20}N/m^2$