Elasticity JEE Main PYQs, 2020 to 2025

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $P \times 10^{11} \, \text{Nm}^{-2}$, where the value of $P$ is: (Take $g = 3\pi \, \text{m/s}^2$)

Two wires A and B are made of same material having ratio of lengths $\frac{L_A}{L_B}=\frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B}=2$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

A steel wire of length 2 m and Young's modulus $2.0 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is __________ $\times 10^5$ (in SI units).

An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is :