ABC is an equilateral triangle with O as its centre. vecF1, vecF2 and vecF3 represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of vecF3 is

Question

ABC is an equilateral triangle with O as its centre. vecF1, vecF2 and vecF3 represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of vecF3 is (A) F1+F2 (B) F1-F2 (C) (F1+F2/2) (D) 2(F1+F2)

Tardigrade Admin · Accepted Answer

Let x be the distance of centre O of equilateral triangle from each side. Total torque about O=0 ⇒ F1 x+F2 x-F3 x=0 or F3=F1+F2

Q. $A BC$ is an equilateral triangle with $O$ as its centre. $F_{1}, F_{2}$ and $F_{3}$ represent three forces acting along the sides $A B, BC$ and $A C$ respectively. If the total torque about $O$ is zero then the magnitude of $F_{3}$ is

$F_{1} + F_{2}$

$F_{1} - F_{2}$

$\frac{F _{1} + F _{2}}{2}$

$2 (F_{1} + F_{2})$

Let $x$ be the distance of centre $O$ of equilateral triangle from each side.
Total torque about $O = 0$
$\Rightarrow F_{1} x + F_{2} x - F_{3} x = 0$
or $F_{3} = F_{1} + F_{2}$

Q. ABC is an equilateral triangle with O as its centre. F1​​,F2​​ and F3​​ represent three forces acting along the sides AB,BC and AC respectively. If the total torque about O is zero then the magnitude of F3​​ is

F1​+F2​

F1​−F2​

2F1​+F2​​

2(F1​+F2​)