Question

In the following diagram, pulley $P _ { 1 }$ is movable and pulley $P _ { 2 }$ is fixed. The value of angle θ will be

• A. 60⁰
• B. 30⁰
• C. 45⁰
• D. 15⁰

Answer 1

Answer: (B)

30⁰

Answer 2

Free body diagram of pulley $P _ { 1 }$ is shown in the figure

For horizontal equilibrium $T _ { 1 } \cos \theta = T _ { 2 } \cos \theta$ $\therefore$ $T _ { 1 } = T _ { 2 }$

and $T _ { 1 } = T _ { 2 } = W$

For vertical equilibrium

$T _ { 1 } \sin \theta + T _ { 2 } \sin \theta = W$ ⇒ $W \sin \theta + W \sin \theta = W$

∴ $\sin \theta = \frac { 1 } { 2 }$ or $\theta = 30 ^ { \circ }$