Question

The sum of two forces is $18N$ and resultant whose direction is at right angles to the smaller force is $12N$. The magnitude of the two forces are

• A. 13, 5
• B. 12, 6
• C. 14, 4
• D. 11, 7

Answer 1

Answer: (A)

13, 5

Answer 2

We have, $|\overset{\rightarrow}{P}| + |\overset{\rightarrow}{Q}| = 18N$; $|\overset{\rightarrow}{R}| = |\overset{\rightarrow}{P} + \overset{\rightarrow}{Q}| = 12N$

$\alpha = 90^{o}$ ⇒ $P + Q\cos\theta = 0$ ⇒ $Q\cos\theta = - P$

Now,$R^{2} = P^{2} + Q^{2} + 2PQ\cos\theta$

⇒$R^{2} = P^{2} + Q^{2} + 2P( - P) = Q^{2} - P^{2}$

⇒ $12^{2} = (P + Q)(Q - P) = 18(Q - P)$

⇒ $Q - P = 8$ and $Q + P = 18$ ⇒ $Q = 13$, $P = 5$

$\therefore$ Magnitude of two forces are 5N, 13N.