question_answer

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

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

B)                 \[({{F}_{1}}-{{F}_{2}})\]                

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

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

Correct Answer: C

Solution :

                Let r be the perpendicular distance of \[{{F}_{1}},{{F}_{2}}\]  and \[{{F}_{3}}\] from O as shown in figure                                 The torque of force \[{{F}_{3}}\] about O is clockwise, while torque due to \[{{F}_{1}}\] and \[{{F}_{2}}\] are anticlockwise.                 For total torque to be zero about O, we must have                 \[{{F}_{1}}r+{{F}_{2}}r-{{F}_{3}}r=0\]                 \[\Rightarrow {{F}_{3}}={{F}_{1}}+{{F}_{2}}\]