Three forces P, Q and R are acting on a particle in the plane, the angle between P and Q and then between Q and R are `150^(@)` and `120^(@)` respectively. Then for equilibrium, forces P, Q and R are in the ratio :

Options

A. `1:2:3`
B. `1:2:sqrt(3)`
C. `3:2:1`
D. `3^(1//2):2:1`

Answer

D

Explanation

`P cos 60^(@)=R cos 30^(@)`
`therefore P=Rsqrt(3)`
`Q=P sin 60^(@)+R sin 30^(@)`
`Q=Rsqrt(3)xxsqrt(3)/(2)+(R)/(2)=2R`
`P:Q:R=sqrt(3):2:1`