
The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in…

- $\quad \cos ^{-1}(1)$
- $\quad \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
- $\cos ^{-1}\left(\frac{1}{2}\right)$
- $\quad \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)$
Solution

$\mathrm{T}=\mathrm{Mg}$ and, For the system to remain in equilibrium, $\begin{array}{ll} & 2 \mathrm{~T} \cos \theta=\sqrt{2} \cdot \mathrm{Mg} \\ \therefore & 2 \mathrm{~T} \cos \theta=\mathrm{T} \sqrt{2} \\ \therefore & \cos \theta=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}} \\ \therefore & \theta=\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \end{array}$
Asked in: MHT CET 2024 (15 May Shift 1)