A particle P is acted by three coplanar forces as shown in the figure

Find the force needed to prevent the particle P from moving.(taking, sqrt(3)=1.7)`

Options

A. `320 N` in the direction of `F_(1)`
B. `200 N` in opposite direction of `F_(2)`
C. `320 N` in opposite direction of `F_(1)`
D. `320 N` at an angle `53^(@)` with direction of `F_(3)`

Answer

C

Explanation

Let applied force is `F_(4)=F_(x)hat(i)+F_(y)hat(j)`
To prevent the particle `P` from moving, net force on the particle will be zero.

`:. SigmaF_(x)=0`
or`SigmaF_(x)=F_(x)+150+200 cos 30^(@)=0`
`:. F_(x)= -150-100sqrt(3)= -(150+170)= -320N`
and `SigmaF_(y)=0`
or `200 sin 30^(@)-100+F_(y)=0`
`:. F_(x)=0`
It means `F_(4)` is direction opposite to `F_(1)`.