Question

The pulley and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be
(a) $0^0$
(b) ${30}^0$

Answer 1

From force diagram shown in figure

$T=mg.......\left(1\right)$

$2T\cos \theta =\sqrt{2}mg$

$T=\frac{\sqrt{2}mg}{2\cos \theta }$

$T=\frac{mg}{\sqrt{2}\cos \theta }.....\left(2\right)$

from eqs(1) and (2)

$2mg\cos \theta =\sqrt{2}mg$

$\cos \theta =\frac{1}{\sqrt{2}}$

$\theta =45°$