Question

The resultant of two forces $P$ and $Q$ is of magnitude $P$. If the force $P$ is doubled, $Q$ remaining the same, then angle between new resultant and the force $Q$ is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$

Suppose the angle between $P$ and $Q$ be $\alpha$.
Since, the resultant of $P$ and $Q$ is $P.$
$\therefore P^2=P^2+Q^2+2PQ\cos \alpha$
$\Rightarrow Q+2P\cos \alpha =0$

Let the angle between new resultant and $Q$ is $\theta$, then
$\tan \theta =\frac{2P\sin \alpha }{Q+2P\cos \alpha }$
$\Rightarrow \theta ={90}^{\circ }(\because Q+2P\cos \alpha =0)$