JEE Advanced 2019 — Paper 1 — Question 12

A block of weight 100 N is suspended by copper and steel wires of same cross sectional area $0.5 \mathrm{~cm}^{2}$ and, length $\sqrt{3} \mathrm{~m}$ and 1 m , respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are $30^{\circ}$ and $60^{\circ}$, respectively. If elongation in copper wire is $\left(\Delta \ell_{C}\right)$ and elongation in steel wire is $\left(\Delta \ell_{\mathrm{S}}\right)$, then the ratio $\frac{\Delta \ell_{\mathrm{C}}}{\Delta \ell_{\mathrm{S}}}$ is $\_\_\_\_$

[Young's modulus for copper and steel are $1 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ and $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$, respectively.]