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.

Options

A. `4/1`
B. `2/1`
C. `1/4`
D. `1/2`

Answer

B

Explanation

`(3Q)^(2)= P^(2)+Q^(2)+2PQ cos theta`
`9Q^(2)= P^(2)+Q^(2)+2PQ cos theta`…..(i)
Also, `Q^(2)=P^(2)+Q^(2)+2PQ cos theta (180-theta)`
`Q^(2)=P^(2)+Q^(2)-2PQ cos theta`….(ii)
Adding (i) and (ii), `10Q^(2)= 2P^(2)+2Q^(2)`
or `8Q^(2)= 2P^(2)`
or `(P_(2))/(Q_(2))= 8/2= 4/1 or P/Q= 2`