ABC is an equilateral with O as its centre `vecF_(1), vecF_(2)` and `vecF_(3)` represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of `vecF_(3)` is :

Options

A. `2(F_(1)+F_(2))`
B. `F_(1)+F_(2)`
C. `F_(1)-F_(2)`
D. `(F_(1)+F_(2))/(2)`

Answer

B

Explanation

Torque = force `xx`perpendicular distance of the line of action of force from axis of rotation.

Torque about a point O due to all the three forces is,
`tau=rF_(1)sin90^(@)+rF_(2)sin90^(@)-rF_(3)sin90^(@)`
If `tau=0`,
`F_(1)+F_(2)-F_(3)=0`
`F_(3)=F_(1)+F_(2)`