Q 11-08-111JEE MainJEE Main 2025 (7 Apr, Shift 1)Easy
Two wires A and B are made of the same material, having ratio of lengths $\dfrac{L_A}{L_B} = \dfrac13$ and their diameters ratio $\dfrac{d_A}{d_B} = 2$. If both the wires are stretched using the same force, what would be the ratio of their respective elongations?
Answer: (B) $1 : 12$
$\Delta L = \dfrac{FL}{AY}$ with $A \propto d^2$; $F$ and $Y$ are the same.
$$\frac{\Delta L_A}{\Delta L_B} = \frac{L_A}{L_B}\left(\frac{d_B}{d_A}\right)^2 = \frac13\times\frac14 = \frac1{12}$$
Solution by Sreeraj P, M.Sc Physics