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 $T_2$ respectively. $T_1$ and $T_2$ are related by $T_1 = \sqrt3\,T_2$. The angles $\theta_1$ and $\theta_2$ are:
Answer: (B) $\theta_1 = 60^\circ,\ \theta_2 = 30^\circ$ with $T_2 = \dfrac{mg}{2}$
Horizontal balance: $T_1\cos\theta_1 = T_2\cos\theta_2 \Rightarrow \sqrt3\cos\theta_1 = \cos\theta_2$.
This holds for $\theta_1 = 60^\circ$, $\theta_2 = 30^\circ$: $\sqrt3\cdot\frac12 = \frac{\sqrt3}{2}$ ✔ (it fails for 30°/60° and 45°/45°).
Vertical balance:
$$T_1\sin60^\circ + T_2\sin30^\circ = mg \Rightarrow T_2\left(\sqrt3\cdot\frac{\sqrt3}{2} + \frac12\right) = 2T_2 = mg \Rightarrow T_2 = \frac{mg}{2}$$
Solution by Sreeraj P, M.Sc Physics