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

The correct option is A $l$

$l=\frac{FL}{\pi r^{2}Y}\Rightarrow \frac{l_2}{l_1}=\frac{F_2}{F_1}\frac{L_2}{L_1}{\left(\frac{r_1}{r_2}\right)}^2=2\times 2\times {\left(\frac{1}{2}\right)}^2=1\therefore l_2=l_1$ i.e. the increment in length will be same.