Question

Figure shows three forces `vec"F"_1,vec"F"_2` and `vec"F"_3` acting along the sides of an equilateral triangle. If the total torque acting at point 'O' (centre of the triangle) is zero then the magnitude of `vec"F"_3` is ______.

Options

• F₁ + F₂

• F₁ - F₂

• `("F"_1-"F"_2)/2`

• `"F"_1/"F"_2`

Answer 1

Figure shows three forces `vec"F"_1,vec"F"_2` and `vec"F"_3` acting along the sides of an equilateral triangle. If the total torque acting at point 'O' (centre of the triangle) is zero then the magnitude of `vec"F"_3` is F₁ + F₂.

Explanation:

Force `vec"F"_1` and `vec"F"_2` produce anticlockwise torques while force `vec"F"_3` produces clockwise torque. The torques in the two directions balance each other. The perpendicular distance of the forces from the centre is the same.

∴ F₁r + F₂r = R₃r or F₁ + F₂ = F₃