Concept:The dual requirements for translational and rotational equilibrium.
Formula:$$\text{Translational Equilibrium: } \Sigma \vec{F} = 0$$
$$\text{Rotational Equilibrium: } \Sigma \vec{\tau} = 0$$
Solution:For a body to remain in complete equilibrium, it must not undergo translational acceleration nor rotational acceleration. This requires both the net external force and the net external torque about any axis to be zero.
Why other options are incorrect:- A is incorrect because satisfying only the first condition allows the body to undergo angular acceleration.
- B is incorrect because satisfying only the second condition allows the body to undergo linear translation.
- D is incorrect because the horizontal and vertical forces being equal does not ensure they sum to zero.
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