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

Options

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

Answer

D

Explanation

The torquues `F_(1)d` and `F_(2)d` of `F_(1)` and `F_(2)` respectively are counterclockwise. The torque `F_(3)d` is clockwise. Applying condition for rotational equilibrium

`F_(1)d+F_(2)d-F_(3)d=0` or `F_(3)=F_(1)+F_(2)`