question_answer

ABC is an equilateral triangle with O as its centre. \[{{F}_{1}},\,\,{{F}_{2}}\,\,and\,\,{{F}_{3}}\] represents three forces acting along the sides AB, BC and AC respectively. If total torque about O is zero, then the magnitude of \[{{F}_{3}}\] is  

A)  \[\frac{{{F}_{1}}\,\,and\,\,{{F}_{2}}}{2}\]                  

B)  \[{{F}_{1}}\,\,-\,\,{{F}_{2}}\]

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

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

Correct Answer: C

Solution :

Let d be distance of centre 0 of equilateral triangle O form each side. \[\operatorname{Total} torque about O = 0\] \[\Rightarrow \,\,\,\,\,\,\,\,\,{{F}_{1}}d+{{F}_{2}}d-{{F}_{3}}d=0\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,{{\operatorname{F}}_{3}}={{F}_{1}}+{{F}_{2}}\]