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NEET 2012 (AIPMT, Prelims) · Torque, Couple & Equilibrium of Rigid Bodies

Torque, Couple & Equilibrium of Rigid Bodies question from NEET 2012 (AIPMT, Prelims)

Q43NEET 2012 · AIPMT · PRELIMSMedium

Torque, Couple & Equilibrium of Rigid Bodies

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 magnitude of $\vec{F_3}$ is

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Answer: (a)

O is equidistant (distance r) from all three sides, so each torque is $F\cdot r$ .
From the figure, $F_1$ (along AB) and $F_2$ (along BC) turn the triangle anticlockwise about O; $F_3$ (along AC) turns it clockwise.
$F_3 r = F_1 r + F_2 r \Rightarrow F_3 = F_1 + F_2$
So the answer is (a).

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