Question

The square of the resultant of two equal forces acting at a point is equal to three times their product. Angle between them is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ }$

Let the magnitude of the force be $F$ and angle between the forces be $\theta$.

Magnitude of resultant of two forces, $R=\sqrt{F^2+F^2+2F.F\cos \theta }$

Squaring both sids, we get $R^2=F^2+F^2+2F^2\cos \theta$

Given : $R^2=3F^2$

$\therefore$ $3F^2=F^2+F^2+2F^2\cos \theta$

Or $1=2\cos \theta$

$\therefore$ $\cos \theta =0.5$

$⟹$ $\theta ={60}^o$