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 elongtion is

• A. $zero$
• B. $0.5l$
• C. $l$
• D. $2l$

Answer 1

The correct option is C $l$

According to Hooke's law

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

where , L = original length of the wire

A = cross- sectional area of the wire

Elongation ,$\Delta =\frac{WL}{E}$

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

$\Delta l=\frac{\frac{WL}{2}}{AE}=\frac{WL}{2AE}=\frac{l}{2}$

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