Condition for Equilibrium of a Rigid Body – Rankers Physics

Torque: Practice Problem & Solution

Assertion (A): The condition of equilibrium for a rigid body is – Translational equilibrium: \( \sum \vec{F} = 0 \) (i.e. sum of all external forces equal to zero). Rotational equilibrium: \( \sum \vec{\tau} = 0 \) (i.e. sum of all external torques equal to zero.) Reason (R): A rigid body must be in equilibrium under the action of two equal and opposite forces.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Torque. Understanding the underlying formula is key to arriving at the correct answer below:

For rigid body equilibrium, both net force and net torque must be zero. Assertion (A) correctly states this.

Reason (R) is false; two equal and opposite forces can form a couple if not collinear, causing rotation and thus not guaranteeing equilibrium.

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