If a body floating in a liquid returns back to its original position, when given a small angular displacement, the body, will be in

Concept:

1. Meta center is the point of intersection of the vertical line passing through new center of buoyancy with vertical axis of the body under very small angular tilt is given to the body.
2. In case of fully submerged bodies, during disturbances, the center of buoyancy remains same point of vertical axis of body, since distribution of liquid does not change after tilting. Hence, M and B coincides.
3. To check the stability of equilibrium, we need to give a small tilt in clockwise direction to body and see what its motion after disturbance.
4. Now, after disturbance if body is try to come its original position than it is stable equilibrium and if does not come to its original position rather it moves further from its equilibrium position than it is in unstable Equilibrium and also if it stays at its new position then it is in neutral equilibrium.

Case – 1: G lies above B

After disturbance, Torque about M or B is in clockwise direction i.e. further rotates away ⇒ Unstable equilibrium

Case 2: G and B coincides:

Torque about M is zero ⇒ It stays its new position ⇒ Neutral equilibrium

Case 3: G lies below B-

On given small lift in clockwise direction, Torque about B or M is in anti-clockwise direction i.e. it tries to come back to original position ⇒ Stable equilibrium.