$A B C$ is an equilateral triangle with $O$ as its centre. $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{

Question

$A B C$ 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 $A B, B C$ and $A C$ respectively. If the total torque about $O$ is zero\ then the magnitude of $\vec{F}_{3}$ is\

Professor PC Thomas Classes · Answer

(a) : Let $x$ be the perpendicular distance of centre $O$ of equilateral triangle from each side.\ Total torque about $O=0$\ $\Rightarrow F_{1} x+F_{2} x-F_{3} x=0$ or $F_{3}=F_{1}+F_{2}$\