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ABC is an equilateral triangle with O as its centre. $\vec F_1$, $\vec F_2$ and $\vec F_3$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of $\vec F_3$ is
A
$2(F_1 + F_2)$
B
$F_1 + F_2$
C
$F_1 - F_2$
D
$\frac{F_1 + F_2}{2}$
Detailed Solution
O is the centre of the equilateral triangle, so its perpendicular distance x from each side is the same.
$F_1$ and $F_2$ turn the triangle in one sense about O, while $F_3$ turns it in the opposite sense.
Net torque zero: $F_1x + F_2x - F_3x = 0$
$F_3 = F_1 + F_2$