Q 11-08-029JEE MainJEE Main 2026 (28 Jan, Shift 1)Easy
Two wires $A$ and $B$ made of different materials of lengths 6.0 cm and 5.4 cm , respectively and area of cross sections $3.0\times10^{-5}\ \text{m}^2$ and $4.5\times10^{-5}\ \text{m}^2$, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x : 3$. The value of $x$ is ______
Answer: (D) 5
$Y = \dfrac{FL}{A\,\Delta L}$. With the same load $F$ and the same extension $\Delta L$, $Y\propto \dfrac LA$:
$$\frac{Y_A}{Y_B} = \frac{L_A}{L_B}\cdot\frac{A_B}{A_A} = \frac{6.0}{5.4}\times\frac{4.5}{3.0} = \frac{27}{16.2} = \frac53$$
So $x = 5$.
Solution by Sreeraj P, M.Sc Physics