Two forces are such that the sum of their magnitudes is 18 N

• Laws of Motion

Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are

1. 10 N, 8 N
2. 12 N, 6 N
3. 13 N, 5 N
4. 16 N, 2 N

Answer

Let two forces be A and B.

A + B = 18

12= √(A² + B² + 2AB cosθ)

tan α= (B sin θ)/(A + Bcosθ)

on substituting α = 90, cos θ = -A/B

Solving, A = 5 N and B = 13 N

The correct option is C.