The following four wires are made of the same material. Which of them will have the largest extension when the same tension is applied?

(1) Length=50 cm, diameter=0.5 mm 

(2) Length=100 cm, diameter=1 mm 

(3) Length=200 cm, diameter=2 mm 

(4) Length=300 cm, diameter=3 mm 

Two wires of copper having length in the ratio of 4: 1 and radii ratio of 1: 4 are stretched by the same force. The ratio of longitudinal strain in the two will be:
1. 1: 16                                             
2. 16: 1
3. 1: 64                                             
4. 64: 1

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 same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

(a) l                                       (b) 2l

(c) $\frac{l}{2}$                                    (d) $\frac{l}{4}$ 

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

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

Hooke's Law is obeyed within:

(1) Elastic limit

(2) Proportionality limit

(3) Breaking point

(4) Freezing point

Given below are two statements: 

A steel wire is 1 m long and 1 mm² in area of cross section. If it takes 200 N to stretch this wire by 1 mm, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10 m to a length of 1002 cm?

1. 1000 N

2. 200 N

3. 400 N

4. 2000 N

What is the percentage increase in length of a wire of diameter 2.5 mm, stretched by a force of 100 kg wt? Young's modulus of elasticity of wire$=12.5\times {10}^{11} \mathrm{dyne}/{\mathrm{cm}}^2$

1. 0.16%

2. 0.32%

3. 0.08%

4. 0.12%

A rod of length l and radius r is held between two rigid walls so that it is not allowed to expand. If its temperature is increased, then the force developed in it is proportional to

1. l

2. $\frac{1}{\mathrm{l}}$

3. ${\mathrm{r}}^2$

4. ${\mathrm{r}}^{-2}$