Question

A wire elongates by $1mm$ when a load $W$ is hung from it. If the wire goes over a pulley and the elongation of the wire will be:

• A. $0.5mm$
• B. $1mm$
• C. $2mm$
• D. $4mm$

Answer 1

The correct option is B $1mm$

$\begin{array}{c}Y=\frac{force\times L}{A\times l}=\frac{WL}{Al}\\ l=\frac{WL}{AY}\end{array}$

Due to pulley arrangement, The length of the wire on each side will be $\frac{L}{2}$ and so the elongation will be $\frac{l}{2}$.

For both sides, the elongation will be $\frac{l}{2}+\frac{l}{2}$ = $l$ = $1$mm