First slide

Mechanical equilibrium force cases

Question

Three forces P, Q and R are acting on a particle in the plane, the angle between P and Q and that between Q and R are $150^{0} and 120^{0} respectivley$ . Then for equilibrium, forces P, Q and R are in the ratio

Moderate

A

1 : 2 : 3
B

1 : 2 : $\sqrt{3}$
C

3 : 2 : 1
D

$\sqrt{3} : 2 : 1$

Solution

The particle is at rest under action of forces P, Q and R.
$∴ Q \sin 60^{0} = P and Q \cos 60^{0} = R$
$\Rightarrow \frac{2}{\sqrt{3}} P = Q and 2 R = Q$
$\Rightarrow P : Q : R = \sqrt{3} : 2 : 1$

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