Young’s modulus — UPSC CSE 2021 Physics PYQ

A light rod of length 100\,\mathrm{cm} is suspended from the ceiling, horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and its cross-section is 0.05\,\mathrm{sq.\ cm} and the other is of brass of cross-section 0.1\,\mathrm{sq.\ cm}. Find the position along the rod at which a weight may be hung to produce

(i) Equal stresses in both the wires,

(ii) Equal strain in both the wires. Young's modulus of elasticity of brass and steel are 1.0 \times 10^{11}\,\mathrm{N/m^2} and 2.0 \times 10^{11}\,\mathrm{N/m^2} respectively.