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

(IIT JEE 2001)

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Free Body Diagram of the block of mass $\sqrt{2}$ m:

Therefore, resolving forces in the vertical direction,
$2Tcos\theta =\sqrt{2}mg.$..........................(1)
Free Body Diagram of block m:

Therefore, $T=mg$...............................(2)

This is also why tension in both strings will be the same.

$\therefore$ from (1) and (2)

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

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

$\Rightarrow \theta ={45}^{\circ }$