Question

Resultant of two forces P and Q is
√3 Q. The resultant
is inclined at 30° with P. Show that, either P = Q or
P = 2Q.(with proper explanation)​

Answer 1

Explanation:

R^2 = P^2 + Q^2 + 2PQ cos θ where θ is the angle between P & Q.

3 Q^2 = P^2 + Q^2 + 2PQ cos θ

2 Q^2 = P^2 + 2PQ cos θ ——————-1

Angle between R and P is π/6

sin π/6 = (1/2) = Q sin θ / R = Q sin θ /( Q √3)

sin θ = √3 /2 => cos θ = (1/2)

From 1

2 Q^2 = P^2 + PQ

P^2 + PQ - 2 Q^2= 0

P = Q and P =- 2 Q