First slide

Torque

Question

O is the centre of an equilateral triangle ABC. ${\vec{F}}_{1}, {\vec{F}}_{2} and {\vec{F}}_{3}$ are three forces acting along the sides AB, BC and AC as shown in figure. What should be the magnitude of ${\vec{F}}_{3}$ so that total torque about O is zero

Moderate

A

$|{\vec{F}}_{3}| = |{\vec{F}}_{1}| + |{\vec{F}}_{2}|$
B

$|{\vec{F}}_{3}| = |{\vec{F}}_{1}| - |{\vec{F}}_{2}|$
C

$|{\vec{F}}_{3}| = {\vec{F}}_{1} + 2 \vec{F_{2}}$
D

Not possible

Solution

Total torque about O $= |{\vec{F}}_{1}| d + |{\vec{F}}_{2}| d - |{\vec{F}}_{3}| d = 0$
$\Rightarrow |{\vec{F}}_{3}| = |{\vec{F}}_{1}| + |{\vec{F}}_{2}|$

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