Question

The pulleys and strings shown in the fig. are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be:

• A. $0^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${60}^o$

Answer 1

The correct option is C ${45}^o$

FBD of $m$
$T=mg......\left(1\right)$
FBD of mass $\sqrt{2}m$
$2Tcos\theta =\sqrt{2}$ mg .....(2)
divide equation (2) by (1) we get $\theta ={45}^o$