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  4. In an equilateral triangle A B C F1 F2 and F3 are three forces acting along the sides A B, B C and A C as shown in the given figure. What should be the magnitude of F3 so that the total torque about O is zero?

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Q. In an equilateral triangle $A B C F_{1} F_{2}$ and $F_{3}$ are three forces acting along the sides $A B, B C$ and $A C$ as shown in the given figure. What should be the magnitude of $F_{3}$ so that the total torque about $O$ is zero?Physics Question Image

Uttarkhand PMTUttarkhand PMT 2004

Solution:

The total torque about $O$ is given by or
$\tau=F_{1} d+F_{2} d-F_{3} d$
$\Rightarrow F_{3}=F_{1}+F_{2}=4+2=6\, N$
Here, $d$ is the perpendicular distance of $O$ from every side of the equilateral triangle.