Three forces P, Q, R are acting at a point in a plane. The angle between P and Q, Q and R are 150° and 120° respectively, then for equilibrium, forces P, Q, R are in the ratio
1. 1 ∶ 2 ∶ 3
2. 1 ∶ 2 ∶ √3
3. 3 ∶ 2 ∶ 1
4. √3 ∶ 2 ∶ 1
1. 1 ∶ 2 ∶ 3
2. 1 ∶ 2 ∶ √3
3. 3 ∶ 2 ∶ 1
4. √3 ∶ 2 ∶ 1
Correct Answer – Option 4 : √3 ∶ 2 ∶ 1
For equilibrium:
\(\dfrac{P}{\sin p} =\dfrac{Q}{\sin q} = \dfrac{R}{\sin r}\)
Where,
p = Angle between Q and R = 120°
r = Angle between P and Q = 150°
q = Angle between P & R = 360° – (120° + 150°)
= 90°
hence,
P ∶ Q ∶ R = sin p ∶ sin q ∶ sin r
= sin 120° ∶ sin 90° ∶ sin 150°
\(=\dfrac{\sqrt{3}}{2} : \dfrac{1}{2} : \dfrac{1}{1}\)
\(\therefore \sqrt{3} : 1 : 2\)