Question 74 of 210

A body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3} T_2$. the angles $\theta_1$ and $\theta_2$ are

A$\theta_1=30^{\circ} \theta_2=60^{\circ}$ with $\mathrm{T}_2=\frac{3 \mathrm{mg}}{4}$B$\theta_1=60^{\circ} \theta_2=30^{\circ}$ with $\mathrm{T}_2=\frac{\mathrm{mg}}{2}$C$\theta_1=45^{\circ} \theta_2=45^{\circ}$ with $\mathrm{T}_2=\frac{3 \mathrm{mg}}{4}$D$\theta_1=30^{\circ} \theta_2=60^{\circ}$ with $\mathrm{T}_2=\frac{4 \mathrm{mg}}{5}$

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Answer: (B) $\theta_1=60^{\circ} \theta_2=30^{\circ}$ with $\mathrm{T}_2=\frac{\mathrm{mg}}{2}$

$\begin{aligned} & \mathrm{T}_1 \sin \theta_1+\mathrm{T}_2 \sin \theta_2=\mathrm{mg} \& \mathrm{~T}_1=\sqrt{3} \mathrm{~T}_2 \\ & \Rightarrow \mathrm{~T}_2\left[\sqrt{3} \sin \theta_1+\sin \theta_2\right]=\mathrm{mg} \\ & \text { for } \theta_1=60^{\circ} \& \theta_2=30^{\circ} \\ & \mathrm{T}_2=\frac{\mathrm{mg}}{2}\end{aligned}$