Question

1. If two numerical equal forces P and p acting at a point produce a resultant force of magnitude
P itself, then the angle between the two original forces is
(A) 0°
(B) 60°
(C) 90°
(D) 120°

with process​

Answer 1

Hey Dear,

● Answer -

(B) θ = 60°

◆ Explanation -

Let P & p be two forces with equal magnitude.

Magnitude of resultant force due to both forces acting at same point is given by -

F = √(P² + 2P.p.cosθ + p²)

But Given that, p = P = F, now -

P = √(P² + 2P.P.cosθ + P²)

P² = 2P² (1 + cosθ)

1 + cosθ = 1/2

cosθ = 1 - 1/2

cosθ = 1/2

Taking cos inverse,

θ = arccos(1/2)

θ = 60°

Therefore, the angle between two original forces is 60°.