Equilibrium of a smooth circular cylinder resting on its curved (convex) surface: A smooth solid cylinder lies on a horizontal surface in contact through its convex curved surface. Classify its equilibrium condition for small disturbances.

Introduction / Context:
Equilibrium of bodies is classified as stable, unstable, or neutral based on the change in potential energy (or center-of-gravity position) when the body is slightly disturbed. Smooth round bodies on flat surfaces are classic illustrations used in engineering mechanics courses.

Given Data / Assumptions:

• Smooth solid circular cylinder on a horizontal plane.
• Contact is along the curved convex surface; negligible friction effects for equilibrium classification.
• Small disturbances (infinitesimal rotations/translations).

Concept / Approach:
If a body, after a small disturbance, tends to return to its original position (potential energy increases with disturbance), equilibrium is stable. If it tends to move further away (potential energy decreases), equilibrium is unstable. If its potential energy does not change to first order (height of centre of gravity remains the same), equilibrium is neutral.

Step-by-Step Solution:

Verification / Alternative check:
The same reasoning explains why a perfect sphere on a horizontal plane is also in neutral equilibrium: any small rotation leaves the centre height unchanged.

Why Other Options Are Wrong:

• Stable/Unstable: would require a rise or drop of the centre of gravity with small rotation, which does not occur here.
• “Out of equilibrium” and “None of these”: incorrect since the body is in equilibrium (no net force/moment initially) and neutral is listed.

Common Pitfalls:
Confusing neutral equilibrium with static indifference due to friction; here, neutrality is a geometric/gravitational property, independent of friction.

Final Answer:
Neutral equilibrium