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

Options

A. 0.5N
B. 1.5N
C. `(sqrt(3))/(4)N`
D. `sqrt(3)N`

Answer

A

Explanation

(a) Minimum additional force needed
`F=-(F_("resultant"))_(x)`
`F_("resultant")=[(4-2)(cos 30 jhatj-sin 30 hati)+( cos 60 hati +sin 60 hatj)]`
`=[2((sqrt(3))/(2)hatj-(1)/(2)hati)+((1)/(2) hati+(sqrt(3))/(2) hatj)]`
`=[(sqrt(3)+(sqrt(3))/(2))hatj+(- hati+(hati)/(2))]`
`=[-(1)/(2)hati+(3sqrt(3))/(2) hatj]=-(1)/(2)+(3sqrt(3))/(2)hatj`
`implies F_(x)=(-( hati)/(2))`
Hence, `|F|=0.5N`