Q 11-03-155JEE MainJEE Main 2019 (10 Jan, Shift 2)Easy
Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta$ is:
Answer: (A) $120^\circ$
$$R^2 = 4F^2 + 9F^2 + 12F^2\cos\theta$$
$$4R^2 = 4F^2 + 36F^2 + 24F^2\cos\theta$$
Substituting the first into the second: $52 + 48\cos\theta = 40 + 24\cos\theta$, so $\cos\theta = -\tfrac12$ and $\theta = 120^\circ$.
Solution by Sreeraj P, M.Sc Physics