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Q.
Two forces $P$ and $Q$ have a resultant perpendicular to $P$ The angle between the forces is
Motion in a Plane
Solution:
The angle made by resultant $(R)$ of the forces $P$ and $Q$ with $P$ is given by
$\tan \theta=\frac{Q \sin \alpha}{P+Q \cos \alpha}$
When $\theta=90^{\circ},$ then $\tan 90^{\circ}=\infty$
$\therefore P+Q \cos \alpha=0$ or $\cos \alpha=-\frac{P}{Q} $ or
$ \alpha=\cos ^{-1}\left(-\frac{P}{Q}\right)$