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

The Correct Option is A

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)
\(\therefore F _{3}= F _{1}+ F _{2}\)