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

Answer 1

Answer: (A)

$l$

Answer 2

Let us consider the length of wire as $L$ and cross-sectional area $A$, the material of wire has Young's modulus as $Y$.

Then for $1\,st$ case, $Y=\frac{w / A}{V L}$
For $2\,nd$ case, $Y=\frac{w / A}{2 l^{'} / L}$
$\therefore l^{'}=\frac{l}{2}$
So, total elongation of both sides $=2 l^{'}=l$