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  4. ABC is an equilateral triangle with O as its centre. vecF1, vecF2 and vecF3 represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of vecF3 is

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Q. $ABC$ 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 $\vec{F_3}$ isPhysics Question Image

AIPMTAIPMT 2012System of Particles and Rotational Motion

Solution:

Let $x$ be the 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 $F_{3}=F_{1}+F_{2}$