question_answer

In 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 the given figure. What should be the magnitude ofF3, so that the total torque about \[O\] is zero ?

A)  2 N                                       

B)  4 N

C)  6 N                                       

D)  8 N

Correct Answer: C

Solution :

                 Torque is defined as \[\tau =\] force \[\times \] perpendicular distance from axis of rotation                 Let a be the distance of forces \[{{F}_{1}},{{F}_{2}},{{F}_{3}}\] from axis of rotation, then total torque is                                 \[\tau ={{F}_{1}}a+{{F}_{2}}\,a-{{F}_{3}}a\] Given,   \[\tau =0\] \[\therefore \]  \[{{F}_{3}}={{F}_{1}}+{{F}_{2}}\] Given,   \[{{F}_{1}}=4N\],  \[{{F}_{2}}=2N\]                                 \[{{F}_{3}}=4N+2N=6N\]