Question

The angle between two forces each equal to $P$ when their resultant is also equal to $P$ is :

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

Answer 1

Answer: (A)

If two forces $F_1$ and $F_2$ are acting at a point at an angle $\theta$, then magnitude $F$ of resultant is
$F=\sqrt{F_1{}^2+F_2{}^2+2F_1{F}_2\cos \theta }$
Given two equal forces and their resultant is also $P$.
$\therefore P=\sqrt{\left(P^2+P^2+2P\times P\times \cos \alpha \right)}=2P\cos \frac{\alpha }{2}$
$\therefore \cos \frac{\alpha }{2}=\frac{1}{2}$ or $\alpha =\frac{2\pi }{3}=120^{\circ }$
Hence, when two forces are equal in magnitude and act at an angle of $120^{\circ }$, then the magnitude of the resultant is
equal to the component force.