Question

A block of weight $100N$ is suspended by copper and steel wires of same cross sectional area $0.5c{m}^2$ and, length $\sqrt{3}m$ and $1m,$ 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 $\left(\Delta I_c\right)$ and elongation in steel wire is $\left(\Delta I_s\right),$ then the ratio $\frac{\Delta I_C}{\Delta l_S}$ is [Young's modulus for copper and steel are $1\times 10^{11}N/m^2$ and $2\times 10^{11}N/m^2,$ respectively]

Answer 1

Answer: 2

$\frac{T_s}{2}=T_c\frac{\sqrt{3}}{2}$
$T_s=\sqrt{3}{T}_c$
$\frac{\Delta {\ell }_c}{\Delta {\ell }_s}=\left(\frac{T_c}{T_s}\right)\left(\frac{{\ell }_C}{{\ell }_S}\right)\left(\frac{Y_S}{Y_C}\right)=\left(\frac{1}{\sqrt{3}}\right)\left(\frac{\sqrt{3}}{1}\right)\left(\frac{2\times {\left(10\right)}^{11}}{1\times {\left(10\right)}^{11}}\right)=2$