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

Answer: (D)

Let the angle between $P$ and $Q$ be $\alpha$ .
Then as resultant of $P$ and $Q$ is $P$.
$\Rightarrow P^2=P^2+Q^2+2PQ\cos \alpha$
$0=Q+2P\cos \alpha$
Let ${}^{\theta }$ be the angle which the new resultant makes with $Q$
Then $\tan \theta =2P\sin \alpha /\left(Q+2P\cos \alpha \right)-1/0=\infty$
$\Rightarrow \theta =90^0$