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Question: The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of t...

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∘60 ^ { \circ }

B

120∘120 ^ { \circ }

C

150∘150 ^ { \circ }

D

90∘90 ^ { \circ }

Answer

120∘120 ^ { \circ }

Explanation

Solution

Let forces are F and 2F and angle between them is θ\theta and resultant makes an angle α\alpha with the force F.

tan⁡α=2Fsin⁡θF+2Fcos⁡θ=tan⁡90\tan \alpha = \frac { 2 F \sin \theta } { F + 2 F \cos \theta } = \tan 90 =∞= \infty

⇒ F+2Fcos⁡θ=0F + 2 F \cos \theta = 0 ∴\therefore cos⁡θ=−1/2\cos \theta = - 1 / 2 or θ=120∘\theta = 120 ^ { \circ }