Question

Three forces $P,Q$ and $R$ are acting on a particle in the plane, the angle between $P$ and $Q$ and $Q$ and $R$ are ${150}^{\circ }$ and ${120}^{\circ }$ respectively. Then for equilibrium, forces $P,Q$ and $R$ are in the ratio

• A. $1:2:3$
  
• B. $\sqrt{3}:2:1$
• C. $3:2:1$
• D. $1:2:\sqrt{3}$

Answer 1

The correct option is B $\sqrt{3}:2:1$

1. Draw a rough diagram of the given problem.

2. Find the ratio of forces $P,Q$ and $R$.

The particle is at rest under action of forces $P,Q$ and $R$.

It is clear from the diagram that

$Q\sin {60}^{\circ }=P$

and

$Q\cos {60}^{\circ }=R$

therefore, $\frac{2}{\sqrt{3}}P=Q$ and $2R=Q$

$\therefore P:Q:R=\sqrt{3}:2:1$

Final answer : (d)