Question

A wire elongates by $1mm$ when a load W is hanged from it. lf 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. $1/2$
• B. $1$
• C. $2$
• D. zero

Answer 1

The correct option is B $1$

Initially the length of wire is $L$

$\therefore$ $Y=\frac{WL}{A\delta L}$ where $\delta L=1mm$

$⟹$ $\frac{WL}{AY}=1mm$ ..................(1)

Now the wire goes over the pulley.

Thus the length of wire on each side of the pulley $L^{\prime }=\frac{L}{2}$

Let the extensions in the wires on the two sides of the pulley be $\delta L_1$ and $\delta L_2$ respectively.

For one side $Y=\frac{WL/2}{A\delta L_1}$

$⟹$ $\delta L_1=\frac{WL}{2AY}=0.5mm$ (using 1)

For another side $Y=\frac{WL/2}{A\delta L_2}$

$⟹$ $\delta L_2=\frac{WL}{2AY}=0.5mm$ (using 1)

Thus total elongation $\delta L_T=0.5+0.5=1mm$