ABC is an equilateral triangle with O as its centre. vec F₁, vec F₂ and vec F₃

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6.System of Particles and Rotational Motion

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$ABC$ 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 the magnitude of $\vec F_3$ is

A

$({F_1} + {F_2})/2$

B

$2\,({F_1} + {F_2})$

C

$({F_1} + {F_2})$

D

$({F_1} - {F_2})$

(AIPMT-1998) (AIPMT-2012)

Solution

Let $x$ be the distance of center $O$ of equilateral triangle from each side.

Total torque about $O = 0$

$ \Rightarrow \,{F_1}x + {F_2}x – {F_3}x = 0\,\,or\,\,{F_3} = {F_1} + {F_2}$

Standard 11

Physics

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