Question

The pulley and string are shown in Fig. smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be

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

Answer 1

The correct option is C ${45}^0$

We know that,

Tension on the string $=mg$ $⟶\left(i\right)$

The component of $T$ which is working $\Rightarrow T\cos \theta$

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

Since there are $2$ blocks,

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

$2\left(mg\right)\cos \theta =\sqrt{2}mg$ (from (i))

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

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

[C] $\theta ={45}^0$