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PQR is a rigid equilateral triangle fram...

`PQR` is a rigid equilateral triangle frame of a side length `L`. Forces `F_1, F_2` and `F_3` are acting along `PQ, QR, PR`. If the system is in rotational equilibrium find the relation between the forces.

Text Solution

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Perpendicular distance of any force from centroid `C` of triangle is `L//2sqrt(3)`. The forces `F_(1),F_(2)` produce anti-clockwise turning effect where as `F_(3)`
clockwise turning effect about `C`

Since the system is in rotational equilibrium the total torque acting on the system about the centroid is zero
`F_(1)xxL/(2sqrt(3))+F_(2)xxL/(2sqrt(3))-F_(3)xxL/(2sqrt(3))=0`
Hence `F_(1)+F_(2)-F_(3)=0 :. F_(3)=F_(1)+F_(2)`
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