Question

The resultant of two forces is equal to the double of magnitude of smaller force and the resultant is perpendicular to the smaller force, what is the angle between the forces?

Answer 1

Let two forces F₁ and F₂ are given
A/C to question,
|F₁| = 2|F₂|
Resultant of two forces F₁ and F₂ are given by
R = F₁ + F₂

A/C to question,
R is perpendicular upon smaller force.
Here smaller force is F₂.
So, R.F₂ = 0
⇒(F₁ + F₂).F₂ = 0
⇒F₁.F₂ + F₂² = 0
⇒|F₁||F₂|cosФ + |F₂|² = 0
Now, put |F₁| = 2|F₂|
⇒2|F₂|.|F₂|cosФ + |F₂|² = 0
⇒2cosФ + 1 = 0
⇒cosФ = -1/2 = cos120°

Hence, angle between two forces is 120°


Hope it helps u........