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. `sqrt(3):2:1`

Answer

D

Explanation

`P/(sin 120^(@))=Q/(sin 90^(@))=R/(sin 150^(@))`
`rArr P/(sqrt(3)//2)=Q/1=R/(1//2)`
`rArr (2P)/sqrt(3)=Q/1=(2R)/1=k` (constant)
`rArr P : Q : R=(sqrt(3)k)/2: k: k/2=sqrt(3):2:1`