Question

If the resultant of two forces of magnitude $p$ and $2p$ is perpendicular to $p$, then the angle between the forces is

• A. $\frac{4\pi }{5}$
  
• B. $\frac{2\pi }{3}$
  
• C. $\frac{5\pi }{6}$
  
• D. $\frac{3\pi }{4}$
  

Answer 1

The correct option is B $\frac{2\pi }{3}$


As given, the angle between resultant of $p$ and $2p$ is ${90}^{\circ }$

$\tan \alpha =\frac{2p\sin \theta }{p+2p\cos \theta }$
$\tan {90}^{\circ }=\frac{2p\sin \theta }{p+2p\cos \theta }$
$\Rightarrow p+2p\cos \theta =0$
$\Rightarrow \cos \theta =-\frac{1}{2}$
$\Rightarrow \theta =\frac{2\pi }{3}$