Question

Two equal forces have the square of their resultant equal to three times their product . find the angle between them.​

Answer 1

Explanation:

Given two forces P and Q, such that | P | = P, | Q | = Q, and P = Q, acting at a point, such that square of magnitude R of resultant R of P and Q is 3 P² = 3 Q². We are required to find the angle between P and Q.

Let the angle between P and Q is ∅. Then by parallelogram law of vectors we have for the resultant, that,

R² = P² + Q² + 2 P Q Cos ∅ = P² + P² + 2 P P Cos ∅= 2 P² + 2 P² Cos ∅. ……..(1)

We are given that R² = 3 P². Substituting for R² in equation 1, we get,

3 P² = 2 P² + 2 P² Cos ∅, or Cos ∅ = ½ or ∅ = 60° .

The angle between the two forces is 60° .

Answer 2

R² = P² + Q² + 2 P Q Cos ∅ = P² + P² + 2 P P Cos ∅= 2 P² + 2 P² Cos ∅ ____(1)

3 P² = 2 P² + 2 P² Cos ∅, or Cos ∅ = ½ or ∅ = 60° .

so 60