Question

The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is (in degrees):

• A. ${60}^{\circ }$
• B. ${90}^{\circ }$
• C. ${120}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

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

Let the two forces be $\overrightarrow{F_1}and\overrightarrow{F_2}with\left|\overrightarrow{F_1}\right|=F_{1}and\left|\overrightarrow{F_2}\right|=F_{2}and{F}_2=2\times F_1\Rightarrow \frac{F_1}{F_2}=\frac{1}{2}=\cos \theta (fromthefig.)\Rightarrow \theta =\pi /3$

Therefore angle between the two vectors$=\pi -\theta =\pi -\pi /3=2\pi /3={120}^0$