Question

Two equal forces$\left(F\right)$ have their resultant equal to either of the forces. Then, at what angle the forces are inclined?

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is D ${120}^{\circ }$

Here ,$|\overrightarrow{A}|=F,|\overrightarrow{B}|=F$

Magnitude of the resultant vector ,$|\overrightarrow{R}|=F$

Let the angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$
Now $|\overrightarrow{R}|=\sqrt{A^2+B^2+2AB\cos \theta }$

$F=\sqrt{F^2+F^2+2F^2\cos \theta }$
$\therefore F=F\sqrt{2(1+\cos \theta )}$

squaring bot sides:
$\Rightarrow 1=2(1+\cos \theta )$
$\therefore \cos \theta =-\frac{1}{2}\Rightarrow \cos \theta =\cos {120}^{\circ }$
$\therefore \theta ={120}^{\circ }$