Two forces P and Q , of magnitude 2 F and 3 F , respectively, are at an angle θ with each other. If the…

Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ is:
  1. 120°
  2. 60°
  3. 30°
  4. 90°

Solution

P→=2F,Q→=3F

R→=P2+Q2+2PQcosθ

=4F2+9F2+12F2cosθ=F13+12cosθ

If Q is doubled

2R→=4F2+36F2+24F2cosθ=F40+24cosθ

413+12cosθ=40+24cosθ

12=-24cosθ

cosθ=-12

θ=120°

Asked in: JEE Main 2019 (10 Jan Shift 2)

Practice more Mathematical Methods questions on Aicharya