The resultant of two forces acting an angle of `120^(@)` is 10 kg wt and is perpendicular to one of the forces .That force is

Options

A. `10sqrt(3)`kg wt
B. `20sqrt(3)` kg wt
C. 10 kg wt
D. `10/sqrt(3)` kg wt

Answer

D

Explanation

Let two forces be `vec(F_(1))` and `vec(F_(2))` inclined at an angle `theta = 120°`. Since resultant force is 10 kg wt and perpendicular to `vec(F_(1))` . So `vec(F_(2))` makes angle with `vec(F)`

`:.F_(2)cos30^@=F`
`F_(2)10/(cos30^@)=(10xx2)/sqrt(3)=20/sqrt(3)kg wt`
Also `F_(2)sin30^@=F_(1)`
`:.F_(1)=20/sqrt(3)xx1/2=10/sqrt(3)`