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)

Stretching force $F=\frac{YA}{L}.\Delta l$ Here, both are of same material (i.e., same Y), same diameter (i.e., same A) and are stretched by same force. So, $\frac{\Delta l_1}{L_1}=\frac{\Delta l_2}{L_2}$ $\therefore$ $\frac{\Delta l_1}{\Delta l_2}=\frac{L_2}{L_2}$ $=\frac{2}{5}$ Work done $W=\frac{1}{2}YA\frac{\Delta l^2}{L}$ Ratio of work done $\frac{W_1}{W_2}={\left(\frac{\Delta l_1}{\Delta l_2}\right)}^2.\frac{L_2}{L_1}$ $={\left(\frac{2}{5}\right)}^2.\left(\frac{5}{2}\right)$ $=\frac{2}{5}$ $=2.5$