Question

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 is :

• A. $ 30^{\circ}$
• B. $ 60^{\circ}$
• C. $ 90^{\circ}$
• D. $ 120^{\circ}$

Answer 1

The Correct Option is D

$4F^2 + 9F^2 + 12F^2 \; \cos \; \theta = R^2$
$4F^2 + 36 \; F^2 + 24 \; F^2 \; \cos \; \theta = 4R^2$
$4F^2 + 36 \; F^2 + 24 \; F^2 \; \cos \; \theta$
$= 4(13F^2 + 12F^2 \cos \theta) = 52 \; F^2 + 48F^2 \cos \theta$
$\cos \theta = \frac{12 F^2}{24 F^2} = - \frac{1}{2}$