Question

$ABC$ 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. $F_1+F_2$
• B. $F_1-F_2$
• C. $\frac{F_1+F_2}{2}$
• D. $2(F_1+F_2)$

Answer 1

Answer: (A)

$F_1+F_2$

Answer 2

The correct option is(A): $F _{1}+ F _{2}$.

Taking anticlockwise torque
$F _{1} d + F _{2} d - F _{3} d =0$
(where $d =$ perpendicular distance of the centre $O$ from each side)
$\therefore F _{3}= F _{1}+ F _{2}$