Question

A block of weight 100 N is suspended by copper and steel wires of same cross sectional area $0.5\, cm^2$ and, length $\sqrt{3}$ 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 $\left(\Delta l_{c}\right)$ and elongation in steel wire is $\left(\Delta l_{s}\right),$ then the ratio $\frac{\Delta l_{c}}{\Delta l_{c}}$ is ___
[Young’s modulus for copper and steel are $1\times10^{11}\,N/m^{2}$ and $2\times10^{11}\,N/m^{2}$, respectively.]

Answer 1

$\frac{T_{1}}{2}=\frac{T_{2}\sqrt{3}}{2}$
$T_{1}=\sqrt{3}T_{2}$
$\frac{\Delta l_{2}}{\Delta l_{1}}=\frac{T_{2}l_{2}}{A_{2}Y_{2}}\times\frac{A_{1}Y_{1}}{T_{1}Y_{1}}$
$\frac{\Delta l_{2}}{\Delta l_{1}}=\frac{\sqrt{3}T_{2}}{T_{1}}\times\frac{2}{1}=2$