• # 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)                 $2\,({{F}_{1}}+{{F}_{2}})$

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                 ${{F}_{1}}r+{{F}_{2}}r-{{F}_{3}}r=0$                 $\Rightarrow {{F}_{3}}={{F}_{1}}+{{F}_{2}}$

You need to login to perform this action.
You will be redirected in 3 sec