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

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

Answer 1

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

Step 1, Given data

One force is double the other in magnitude

The magnitude is perpendicular to the smaller force.

Step 2, Finding the angle between the forces

Let the forces be $F$ and $2F$ and angle between them is $\theta$ and resultant makes an angle $\alpha$ with the force $F$

Now, we have
$\tan \alpha =\frac{2F\sin \theta }{F+2F\cos \theta }=\tan {90}^{\circ }\to \infty$
$\Rightarrow F+2F\cos \theta =0\Rightarrow \cos \theta =\frac{-1}{2}$
$\Rightarrow \theta ={\cos }^{-1}\left(\frac{-1}{2}\right)={120}^{\circ }$

Hence the angle between the forces is ${120}^0$