Question

Two forces, of equal magnitude $P,$ are inclined at angle $\alpha$ with each other. If the resultant is also $P,$ then the angle $\alpha$ (in degree) is

• A. $30°$
• B. $45°$
• C. $60°$
• D. $120°$

Answer 1

The correct option is D $120°$

Let two forces be ${\overrightarrow{F}}_1$ and ${\overrightarrow{F}}_2$ having resultant ${\overrightarrow{F}}_1+{\overrightarrow{F}}_2$
Given, $|{\overrightarrow{F}}_1|=|{\overrightarrow{F}}_2|=|{\overrightarrow{F}}_1+{\overrightarrow{F}}_2|=P$
$\therefore P=\sqrt{P^2+P^2+2\times P\times P\cos \alpha }\Rightarrow P^2=2P^2+2P^2\cos \theta \Rightarrow \cos \theta =-\frac{1}{2}\Rightarrow \theta =120°$