Question

Forces M and N acting at a point O make an angle 150°. Their resultant acts at O has magnitude 2 units and is perpendicular to M. Then, in the same unit, the magnitudes of M and N are

• A. $2\sqrt{3},4$
• B. $\sqrt{\frac{3}{2}},2$
• C. 3, 4
• D.
  4. 5

Answer 1

Answer: (A)

$2\sqrt{3},4$

Answer 2

We have, $2^{2} = M^{2} + N^{2} + 2MN\cos 150{^\circ}$

⇒ $4 = M^{2} + N^{2} - \sqrt{3}MN$ .....(i)

and, $\tan\frac{\pi}{2} = \frac{M\sin 150{^\circ}}{M + N\cos 150{^\circ}} \Rightarrow M + N\cos 150{^\circ} = 0$

⇒ $M - N\frac{\sqrt{3}}{2} = 0$⇒ $M = \frac{N\sqrt{3}}{2}$ .....(ii)

Solving (i) and (ii), we get $M = 2\sqrt{3}$ and $N = 4$.