Question

Two wires of same material and same diameter have lengths in the ratio $2:5$. They are stretched by same force. The ratio of work done in stretching them is

• A. 5 : 2
• B. 2 : 5
• C. 1 : 3
• D. 3 : 1

Answer 1

Answer: (B)

Work Done $=\frac{1}{2} \times$ Force $\times$ Elongation
$Y =\frac{ F l}{ A \Delta l}$
$\Delta l=\frac{F l}{A Y}$
$W$ ork Done $=\frac{1}{2} \times F \times \frac{ F l}{ AY }=\frac{ F ^{2} L }{2 AY }$
Since, the Force, Area and young's modulus is same,
$\therefore $ Work Done $\alpha$ length
$\frac{ W _{1}}{ W _{2}}=\frac{l_{1}}{l_{2}}=\frac{2}{5}$