Question

Two forces of magnitudes P and Q are inclined at an angle `(theta)`. The magnitude of their resultant is 3Q. When the inclination is changed to `(180^(@)-theta)`, the magnitude of the resultant force becomes Q. Find the ratio of the forces.

Answer 1

Correct Answer - `P/Q=2`
`(3Q^(2))=P^(2)+Q^(2)+2PQ cos theta`..(i)
`Q^(2)=P^(2)+Q^(2)+2PQ cos theta(180^(@)-theta)`..(ii)
`9Q^(2)=P^(2)+Q^(2)+2PQ cos theta`
Adding `10Q^(2)=2P^(2)+2Q^(2)`
or `8Q^(2)=2P^(2)`
`P^(2)/Q^(2)=8/2=4/1` or `P/Q =2`