Question

The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the, magnitudes of forces

• A. 12, 5
• B. 14, 4
• C. 5, 13
• D. 10, 8

Answer 1

Answer: (C)

5, 13

Answer 2

Let P be the smaller force and Q be the greater force then according to problem –

P + Q = 18 ......(i)

$R = \sqrt{P^{2} + Q^{2} + 2PQ\cos\theta} = 12$ .......(ii)

$\tan\varphi = \frac{Q\sin\theta}{P + Q\cos\theta} = \tan 90 = \infty$

∴ $P\ + \ Q\text{ cos}\theta = 0$ .......(iii)

By solving (i), (ii) and (iii) we will get $P = 5,$ and $Q = 13$