Three froces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

Options

A. `(sqrt3)/(4)N`
B. `sqrt3N`
C. `0.5N`
D. `1.5N`

Answer

C

Explanation

4N nad 2N are opposite
So net `=4-2=2N`
Now figure becomes

Horizontal component of 2N along `-ve`
x-direction is `x_(1)=2 sin 30^(@)=1N`
Horizontal component of 1 N along `+ve`
x-direction is `x_(2)=1 cos 60^(@)=(1)/(2)N`
So, net horizontal force is `(1)/(2)N` along `-ve`
x-direction. hence `(1)/(2)` N is required in `+ve`
x-direction