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The resultant of two forces acting an an...

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

A

`10sqrt(3)`kg wt

B

`20sqrt(3)` kg wt

C

10 kg wt

D

`10/sqrt(3)` kg wt

Text Solution

Verified by Experts

The correct Answer is:
D
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)`
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  • The resultant of two forces, one double than the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is :

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