A smooth cylinder lying on its convex surface remains

ANS:B - in unstable equilibrium

1. Equilibrium: Equilibrium refers to a state where the net force acting on an object is zero, and there is no tendency for it to accelerate in any direction. In other words, the object is balanced, and its motion remains unchanged unless acted upon by an external force.
2. Stable Equilibrium: In stable equilibrium, if the object is displaced slightly from its equilibrium position, it experiences a restoring force that brings it back towards the equilibrium position. It tends to return to its original position if disturbed slightly.
3. Unstable Equilibrium: In contrast, unstable equilibrium describes a situation where the equilibrium is delicate. If the object is displaced slightly from its equilibrium position, the restoring force pushes it further away from the equilibrium position. In other words, any small perturbation leads to an amplification of that perturbation, causing the object to move farther away from its original position.

In the case of a smooth cylinder lying on its convex surface, it remains in unstable equilibrium. If the cylinder is disturbed slightly from its balanced position, it will tend to roll further away from that position due to the convex shape of its surface. There is no restoring force that brings it back to its initial position. Instead, the disturbance amplifies, causing the cylinder to move away from its original position.