Two forces of equal magnitude act at a point. Square . . .

Question : Two forces of equal magnitude act at a point. Square of their resultant is 3 times of product of their magnitude. The angle between the force is _______ (in degrees).

Doubt by Suhani

Solution :

F₁=F₂=F (Let)

R²=3[F₁×F₂]

[√(F₁²+F₂²+2F₁F₂cosθ)]²=3[F₁×F₂]
[∵R=√[A²+B²+2ABcosθ]

F₁²+F₂²+2F₁F₂cosθ = 3[F₁×F₂]
F²+F²+2F×Fcosθ = 3[F×F]

[∵F₁=F₂=F]
2F²+2F²cosθ = 3F²
2F²(1+cosθ) = 3F²
1+cosθ=3F²/2F²
1+cosθ=3/2
cosθ=3/2 - 1
cosθ = (3-2)/2
cosθ = 1/2
cosθ = cos60°
θ=60°

Hence, the angle between the two forces is 60°