Question

Figure shows three forces \( F_1, F_2, F_3 \) 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 \( F_3 \) is

• A. \( \frac{F_1 - F_2}{2} \)
• B. \( F_1 - F_2 \)
• C. \( F_1 + F_2 \)
• D. \( \frac{F_1}{F_2} \)

Hint:

For equilibrium of forces and torques, the sum of forces in a system must balance. In this case, \( F_3 = F_1 + F_2 \) ensures no net torque.

Answer 1

The Correct Option is C

Step 1: Understanding the situation.
In an equilateral triangle, when three forces \( F_1, F_2, F_3 \) are acting along the sides, the total torque at the center 'O' should be zero for equilibrium.

Step 2: Balancing the forces.
For the torques to balance and result in zero net torque, the forces must be arranged such that the sum of the forces \( F_3 \) equals the sum of \( F_1 \) and \( F_2 \). Thus, the magnitude of \( F_3 \) is \( F_1 + F_2 \).

Step 3: Conclusion.
The correct answer is \( F_3 = F_1 + F_2 \), which balances the torques and results in no net torque at the center.