Q 11-08-097JEE MainJEE Main 2019 (8 Apr, Shift 2)Easy
Young's moduli of two wires A and B are in the ratio $7:4$. Wire A is $2\ \text{m}$ long and has radius $R$. Wire B is $1.5\ \text{m}$ long and has radius $2\ \text{mm}$. If the two wires stretch by the same length for a given load, the value of $R$ is close to
Answer: (D) $1.7\ \text{mm}$
Extension $\Delta l = \dfrac{FL}{\pi r^2Y}$. Equal extensions under the same load:
$$\frac{L_A}{R^2Y_A} = \frac{L_B}{r_B^2Y_B} \Rightarrow R^2 = r_B^2\cdot\frac{L_A}{L_B}\cdot\frac{Y_B}{Y_A} = 4\times\frac{2}{1.5}\times\frac47 = 3.05\ \text{mm}^2$$
$$R \approx 1.7\ \text{mm}$$
Solution by Sreeraj P, M.Sc Physics