question_answer

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) \[2({{F}_{1}}+{{F}_{2}})\]

B) \[{{F}_{1}}+{{F}_{2}}\]

C) \[{{F}_{1}}-{{F}_{2}}\]

D) \[\frac{{{F}_{1}}+{{F}_{2}}}{2}\]

Correct Answer: B

Solution :

 Taking torque about O, net torque should be zero. \[{{F}_{2}}\times x-{{F}_{3}}\times x+{{F}_{1}}\times x=0\]