| ABC is an equilateral triangle with O as its centre. \[{{F}_{1}},{{F}_{2}}\] and \[{{F}_{3}}\] represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of \[{{F}_{3}}\] is [AIPMT (S) 2012] |
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A) \[{{F}_{1}}+{{F}_{2}}\]
B) \[{{F}_{1}}-{{F}_{2}}\]
C) \[\frac{{{F}_{1}}+{{F}_{2}}}{2}\]
D) \[2({{F}_{1}}+{{F}_{2}})\]
Correct Answer: A
Solution :
| If we take clockwise torque |
| \[\tau ={{\tau }_{{{F}_{1}}}}+{{\tau }_{{{F}_{2}}}}+{{\tau }_{{{F}_{3}}}}\] |
| \[0={{F}_{1}}r+{{F}_{2}}r+{{F}_{3}}r\] |
| \[{{F}_{3}}={{F}_{1}}+{{F}_{2}}\] |
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