Question

A wire elongates by $lmm$ 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 wire will be (in $mm$).

• A. $l/2$
• B. $l$
• C. $2l$
• D. Zero

Answer 1

The correct option is B $l$

$\begin{array}{cc}T& =W\\ T& =YA\left(\frac{\Delta L}{L}\right)\\ & \Delta L=\frac{TL}{Y_A}=\frac{WL}{YA}=lmm\end{array}$

$\begin{array}{c}T=W\\ W=YA\left(\frac{\Delta L^{\prime }}{L/2}\right)\\ \therefore \Delta L^{\prime }=\frac{WL}{2AY}=\frac{l}{2}\end{array}$

$\begin{array}{c}\text{Total elongation in}\\ \text{second case is}2\Delta L\\ =lmm\end{array}$