Q.How do you distinguish between stable and unstable equilibrium?

A system in equilibrium can be stable (returns after a small disturbance), unstable (moves further away after a disturbance), or neutral (stays wherever it's moved to), depending on how its potential energy changes with position.

A body is said to be in equilibrium when the net force and net torque on it are both zero. However, equilibrium can be classified into three types based on what happens when the body is given a small displacement from that equilibrium position:

1. Stable equilibrium: If, when displaced slightly, a restoring force or torque arises that brings the body back toward its original equilibrium position, the equilibrium is called stable. This corresponds to the body's potential energy being at a MINIMUM at the equilibrium position — any small displacement raises the potential energy, and the resulting force pushes the body back down toward the minimum.

   Example: A marble resting at the bottom of a curved bowl. If nudged slightly, gravity pulls it back down toward the bottom.

2. Unstable equilibrium: If, when displaced slightly, a force or torque arises that pushes the body further away from its original position, the equilibrium is called unstable. This corresponds to the potential energy being at a MAXIMUM at the equilibrium position — any small displacement lowers the potential energy, and the body accelerates away from the original position.

   Example: A marble balanced precisely at the top of a smooth, curved hill. The slightest nudge sends it rolling away down the slope.

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