Question

Two wires of the same diameter and of the same material have the length $l$ and $2l$. If the force $F$ is applied on each, the ratio of the work done in the two wires will be

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

Answer 1

The correct option is A

$1:2$
Given,
Length of the first wire, $l_1=l$
Length of the second wire, $l_2=2l$
As given, force for both wires is same. Therefore, work done is directory proportional to length of wire.
Hence,
$W=\frac{1}{2}Fl$
$W\alpha l$
$\frac{W_1}{W_2}=\frac{l_1}{l_2}=\frac{l}{2l}=\frac{1}{2}$

The ratio for work done in both wires will be $1:2$