A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of the same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

1. l                                       

2. 2l

3. $\frac{l}{2}$                                   

4. $\frac{l}{4}$ 

In steel, Young's modulus and the strain at the breaking point are $2\times {10}^{11} {\mathrm{Nm}}^{-2}$ and 0.15 respectively. The stress at the breaking point for steel is, therefore:

1. $1.33\times {10}^{11}N{m}^{-2}$           

2. $1.33\times {10}^{12}N{m}^{-2}$

3. $7.5\times {10}^{-13}N{m}^{-2}$           

4. $3\times {10}^{10}N{m}^{-2}$

The possible value of Poisson's ratio is

1. 1                                       

2. 0.9

3. 0.8                                     

4. 0.4

When a weight of 10 kg is suspended from a copper wire of length 3 metres and diameter 0.4 mm, its length increases by 2.4 cm. If the diameter of the wire is doubled, then the extension in its length will be

1. 9.6 cm                               

2. 4.8 cm

3. 1.2 cm                              

4. 0.6 cm

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 will be:

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 should now be, in mm

1.   1.75                                  

2.   1.5

3.   2.5                                   

4.   5.0

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 maximum extension in the wire, if 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