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Balanced and Unbalanced Forces

C is the cent...

Question

C is the centre of an equilateral triangle PQR. $f_{1}, f_{2}$ and $f_{3}$ are the three forces acting along the sides as shown. For the total torque about C to be zero,

f_{3} = \frac{(f_{1} + f_{2})}{2}

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f_{3} = \frac{(f_{1} + f_{2})}{4}

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f_{3} = f_{1} + f_{2}

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f_{3} = f_{1} - f_{2}

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Solution

The correct option is C $f_{3} = f_{1} + f_{2}$
Both $f_{1}$ and $f_{2}$ exert counter-clockwise torque on the on the triangle about point O while $f_{3}$ exerts clockwise torque about point O. The perpendicular distances from point O on the forces are equal by symmetry.
Let the distance be $l$ .
$∴ f_{1} l + f_{2} l - f_{3} l = 0$
$\Rightarrow f_{1} + f_{2} = f_{3}$

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C is the centre of an equilateral triangle PQR. f1,f2 and f3 are the three forces acting along the sides as shown. For the total torque about C to be zero,

The correct option is C f3=f1+f2Both f1 and f2 exert counter-clockwise torque on the on the triangle about point O while f3 exerts clockwise torque about point O. The perpendicular distances from point O on the forces are equal by symmetry.Let the distance be l.∴f1l+f2l−f3l=0⇒f1+f2=f3

C is the centre of an equilateral triangle PQR. $f_{1}, f_{2}$ and $f_{3}$ are the three forces acting along the sides as shown. For the total torque about C to be zero,