Question

Two wires of same diameter and made of the same material are having the length $1m$ and $2m$ . If the force $F$ is applied on each end of the wires, the ratio of the work done in the two wires will be

• A. $1:2$
• B. $1:4$
• C. $3:1$
• D. $1:1$

Answer 1

The correct option is A $1:2$

Wires are of same material (same Young's modulus) and same diameter (same area). Also, applied forces is same which means$Y,A,F$ is constant
Now,
$Y=\left(\frac{FL}{Al}\right)$Where, $l$ is extension in wire and $L$ is the length of wire. Now,
$l=\left(\frac{FL}{AY}\right)\Rightarrow l\propto L$
We know that, the work done
$W=\frac{1}{2}\times Stress\times Strain\times Volume=\frac{1}{2}\times F\times l\Rightarrow W\propto l$
$\therefore \frac{W_1}{W_2}=\frac{L_1}{L_2}=\frac{1}{2}$