Question

In the following diagram, pulley $P_1$ is movable and pulley $P_2$ is fixed. The value of angle $\theta$ in case of equilbrium will be

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

Free body diagram of pulley $P_1$ is shown in the figure
For horizontal equilibrium $T_1\cos \theta =T_2\cos \theta \therefore T_1=T_2\text{and}{T}_1=T_2=W$

For vertical equilibrium
$T_1\sin \theta +T_2\sin \theta =W\Rightarrow W\sin \theta +W\sin \theta =W$
$\therefore \sin \theta =\frac{1}{2}\text{or}\theta ={30}^{\circ }$