Question

The square of resultant of two equal forces is three times their product. Angle between the forces is:

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

Answer 1

The correct option is D $\frac{\pi }{3}$

Let $\varphi$ be the angle between the forces.

Thus, $F_{net}^2=F_1^2+F_2^2+2F_1{F}_{2}cos\varphi =3F_1{F}_2$
$⟹F^2+F^2+2F^{2}cos\varphi =3F^2$

$⟹cos\varphi =\frac{1}{2}$

$⟹\varphi =\frac{\pi }{3}$