Question

If the centre of gravity of the body lies above the metacentre, then the body is said to be in_____
(A) Stable equilibrium
(B) Unstable equilibrium
(C) Neutral equilibrium
(D) Both (B) and (C)

Answer 1

When the metacentric height of a floating body is positive, then the body is said to be in stable equilibrium. But if the metacentric height is negative, the body is in unstable equilibrium. The metacentric height is measured with reference to the centre of gravity.

Complete step by step solution:
A body floating inside a liquid is acted upon by two forces; the downward weight of the body, and the upward buoyant force. We know that the weight of a body acts on its centre of gravity. Similarly there exists a centre of buoyancy on which the buoyant force acts. At equilibrium, the buoyant force is equal to the weight of the body. Also, these two centres lie along the same vertical line so that the net torque on the body is equal to zero.
Now, if the body is slightly displaced, then the centre of gravity remains at its original position but the centre of buoyancy shifts a little so that these two are not along the same vertical line and hence constitute a couple which produces net torque on the body. If the net torque brings back the body towards its equilibrium position, then the body is said to be in stable equilibrium. But if the net torque rotates the body away from the equilibrium position, then the body is said to be in unstable equilibrium.
The stability of a floating body is decided by the height of the metacentre above the centre of gravity.
If the metacentric height is positive, then the body is said to be in stable equilibrium. But if the metacentric height is negative, then the body is said to be in unstable equilibrium. Also, if the metacentric height is equal to zero, then the body is in neutral equilibrium.
According to the question, the centre of gravity is lying above its metacentre. This means that the metacentre should lie below the centre of gravity. So the metacentric height is negative and therefore the body is in unstable equilibrium.
Hence, the correct answer is option B.

Note
Metacentre of a floating body is the point of intersection of the line joining the centre of gravity and the original centre of buoyancy, and the vertical line through the new centre of buoyancy. It is very easy to make out when the metacentre is above the below of gravity, then the resulting torque produced will turn the body away from the equilibrium position.