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Q.
The angle between two forces each equal to $P$ when their resultant is also equal to $P$ is :
Vector Algebra
Solution:
If two forces $F_{1}$ and $F _{2}$ are acting at a point at an angle $\theta$, then magnitude $F$ of resultant is
$F =\sqrt{ F _{1}{ }^{2}+ F _{2}{ }^{2}+2 F _{1} F _{2} \cos \theta}$
Given two equal forces and their resultant is also $P$.
$\therefore P=\sqrt{\left(P^{2}+P^{2}+2 P \times P \times \cos \alpha\right)}=2 P \cos \frac{\alpha}{2}$
$\therefore \cos \frac{\alpha}{2}=\frac{1}{2}$ 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.