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
$Y=\frac{Fl}{A\Delta l}$
$\Delta l=\frac{Fl}{AY}$
$W$ ork Done $=\frac{1}{2}\times F\times \frac{Fl}{AY}=\frac{F^{2}L}{2AY}$
Since, the Force, Area and young's modulus is same,
$\therefore$ Work Done $\alpha$ length
$\frac{W_1}{W_2}=\frac{l_1}{l_2}=\frac{2}{5}$