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$A B C$ is an equilateral triangle with $O$ as its centre. $\mathrm{F}_1, \mathrm{~F}_2$ and $\mathrm{F}_3$ 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 $\mathrm{F}_3$ is
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Verified Answer
The correct answer is:
$F_1+F_2$
If we take clockwise torque
$\begin{aligned}
\tau & =\tau_{F_1}+\tau_{F_2}+\tau_{F_3} \\
0 & =F_1 r+F_2 r+F_3 r \\
F_3 & =F_1+F_2
\end{aligned}$
$\begin{aligned}
\tau & =\tau_{F_1}+\tau_{F_2}+\tau_{F_3} \\
0 & =F_1 r+F_2 r+F_3 r \\
F_3 & =F_1+F_2
\end{aligned}$
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