Question

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. $\frac{l}{4}$

Answer 1

Answer: (A)

l

Answer 2

(1)

$l = \frac{FL}{\pi r^{2}Y}$ Ž $\frac{l_{2}}{l_{1}} = \frac{F_{2}}{F_{1}}\frac{L_{2}}{L_{1}}\left( \frac{r_{1}}{r_{2}} \right)^{2} = 2 \times 2 \times \left( \frac{1}{2} \right)^{2} = 1$

$\therefore l_{2} = l_{1}$ i.e. the increment in length will be same