Question

Two forces of magnitudes P and Q are inclined at an angle $(θ)$ the magnitude of their resultant is 3Q. When the inclination is changed to (180- $θ$ ) the magnitude of the resultant force between Q. The ratio of the forces ( $\frac{P}{Q}$ ) is

Moderate

Solution

${(3 Q)}^{2} = P^{2} + Q^{2} + 2 PQcosθ$
$9 Q^{2} = P^{2} + Q^{2} + 2 PQcosθ$ ------(i)
Also, $Q^{2} = P^{2} + Q^{2} + 2 PQcosθ (180 - θ)$
$Q^{2} = P^{2} + Q^{2} - 2 PQcosθ - - - - (ii)$
Adding (i) and (ii), $10 Q^{2} = 2 P^{2} + 2 Q^{2}$
or $8 Q^{2} = 2 P^{2}$
$or \frac{P^{2}}{Q^{2}} = \frac{8}{2} = \frac{4}{1} or \frac{P}{Q} = 2$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

SCAN ME