Q 11-08-049JEE MainJEE Main 2023 (30 Jan, Shift 2)Easy
A force is applied to a steel wire $A$, rigidly clamped at one end. As a result elongation in the wire is $0.2\ \text{mm}$. If same force is applied to another steel wire $B$ of double the length and a diameter $2.4$ times that of the wire $A$, the elongation in the wire $B$ will be (wires having uniform circular cross sections)
Answer: (D) $6.9\times10^{-2}\ \text{mm}$
$\Delta L=\dfrac{FL}{AY}\propto\dfrac{L}{d^2}$.
$$\Delta L_B=0.2\times\frac{2}{(2.4)^2}=\frac{0.4}{5.76}=0.069\ \text{mm}=6.9\times10^{-2}\ \text{mm}$$
Solution by Sreeraj P, M.Sc Physics