Question

The sum of the two forces is 8 kg wt and the magnitude of the resultant which is at right angles to the smaller force is 4 kgwt. Find the two forces.

Answer 1

Let P be the smaller force.

P + Q = 8 kg wt.,

a = 90°, R = 4 kg wt.,

tan α = \(\frac {Qsin \theta}{P+Qcos \theta}\)

tan 90° = \(\frac {Qsin \theta}{P+Qcos \theta}\)

∞ =\(\frac {Qsin \theta}{P+Qcos \theta}\)

⇒ P + Q cosθ = 0

cosθ = \(\frac {-P}{Q}\)

Q² - P² = 16

(Q-P)(Q+P) = 16

(Q-P) × 8 = 16

Q - P = 2

P + Q = 8

∴ 2Q = 10 

⇒ Q = 5 kg wt. and P 

= 3 kg wt.