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Three forces are acting on a particle as...

Three forces are acting on a particle as shown in the figure. To have the resultant force only along the Y-direction, the magnitude of the minimum additional force needed is

A

`0.5 N`

B

`1.5 N`

C

`(sqrt(3))/4 N`

D

`sqrt(3)N`

Text Solution

Verified by Experts

The correct Answer is:
A
The component of `1N`and `2N` forces along +x axis `= (1cos 60^(@)= 2 sin 30^(@))`

`=1xx1/2+2xx1/2=1/2+1=3/2= 1.5N`
The component of `4 N` forces along x-axis.
`= 4sin 30^(@)= 4xx1/2= 2 N`
Hence net x-component of resultant
`F_(x)= -2+1.5= -0.5 N` along -x direction
Therefore, if a force of `0.5 N` is applied along +x-axis, the resultant force along x-axis will become zero and the resultant force will be obtained only along y-axis.
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