Question

If the resultant of two forces of magnitude P and 2P is perpendicular to P, then the angle between the forces is

• A. $2\pi /3$
• B. $3\pi /4$
• C. $4\pi /5$
• D. $5\pi /6$

Answer 1

The correct option is A

$2\pi /3$

Step 1: Given data

The resultant of two forces of magnitude P and 2P is perpendicular to P.

Step 2: To find

Then the angle between the forces is?

Step 3: Calculation

Let R be the resultant,

$$\begin{gathered} \tan \theta =\frac{2P\sin \alpha }{P+2P\cos \alpha } \\ \tan 90°=\frac{2P\sin \alpha }{P+2P\cos \alpha } \\ \infty =\frac{2P\sin \alpha }{P+2P\cos \alpha } \\ \Rightarrow P+2P\cos \alpha =0 \\ \Rightarrow 2P\cos \alpha =-P \\ \Rightarrow \cos \alpha =\frac{-1}{2} \\ \Rightarrow \alpha =120° \\ \alpha =\frac{2\pi }{3} \end{gathered}$$

Hence, option A is correct.