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