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. $2\times {10}^{-7}N$

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 = $0.9\times {10}^{11}N/m^2$)

1. Nearly 17 N                       
2  Nearly 34 N
3. Nearly 51 N                        
4. 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:

1. 1.75                                  
2. 1.5
3. 2.5                                   
4. 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