Question

A wire elongates by $l$ $mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $mm$):

• A. $1$
• B. $2l$
• C. zero
• D. $l/2$

Answer 1

The correct option is A $1$

According to hook's law

Modules of elasticity $,E=\frac{W}{A}\times \frac{l}{1}$

where$,$ $l=$ original length of the wire

$A=$ cross sectional area of the wire

$\therefore Elongation,\Delta l=\frac{Wl}{E}$

on either side of the wire$,$ tension is $W$ and length is $\frac{1}{2}$

$\Delta l=\frac{Wl}{\frac{2}{AE}}=\frac{Wl}{2AE}=\frac{1}{2}$

$\therefore$ Total elongation in the wire $\frac{1}{2}+\frac{1}{2}=1$

Hence,

option $\left(A\right)$ is correct answer.