Equilibrium, Third Law & Frames question from MHT CET 2024 (15 May, Shift 1)

Answer: (d)

1. Each string over a smooth pulley has tension $T = Mg$.
2. Both strings make angle $\theta$ with the vertical at the middle block, so vertically $2Mg\cos\theta = \sqrt{2}Mg$.
3. $\cos\theta = \frac{1}{\sqrt{2}}$
4. So the answer is (d) $\cos^{-1}\left(\frac{1}{\sqrt{2}}\right)$.