Question

The pulleys 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. $45 ^\circ $
• B. $60 ^\circ $
• C. $0 ^\circ $
• D. $30 ^\circ $

Answer 1

Answer: (A)

The tension in both the strings will be same.

For equilibrium in vertical direction for body $B$ we have
$\sqrt{2} m g = 2 T \cos \theta $
$\therefore \, \, \sqrt{2} m g = 2 \left( m g \right) \cos \theta $
( $\because \, \, T = m g$ at equilibrium)
$\therefore \, \, \cos \theta = \frac{1}{\sqrt{2}} \, \, \Rightarrow \theta = 45 ^\circ $