question_answer

O is the centre of an equilateral triangle ABC. \[{{F}_{1}},\text{ }{{F}_{2}}\] 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?

[AIPMT 1998]

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

\[{{F}_{1}}r+{{F}_{2}}r-{{F}_{3}}r=0\]

\[\Rightarrow \]   \[{{F}_{3}}={{F}_{1}}+{{F}_{2}}\]