First slide

Equilibrium of a particle

Question

In the following diagram, pulley P₁ is movable and pulley P₂ is fixed. The value of angle $θ$ will be

Moderate

A

60^o
B

30^o
C

45^o
D

15^o

Solution

From free body diagram of pulley P₁
At the pulley is in equilibrium, considering horizontal direction
For horizontal equilibrium,
$\begin{array}{l} T_{1} \cos θ = T_{2} \cos θ \\ \Rightarrow T_{1} = T_{2} and T_{1} = T_{2} = W . . . . . . . (i) \end{array}$
Now considering for vertical equilibrium
$T_{1} \sin θ + T_{2} \sin θ = W . . . . (ii)$
From (i) & (ii), we get
$\begin{array}{l} W \sin θ + W \sin θ = W \\ ∴ \sin θ = \frac{1}{2} or θ = 30^{\circ} \end{array}$

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