Question

For a floating body to be in stable equilibrium, its metacenter should be:
(A) below the center of gravity
(B) below the center of buoyancy
(C) above the center of buoyancy
(D) above the center of gravity

Answer 1

Hint: Whenever the body is floating in liquid, it will experience the upwards force on it which is equal to the weight of the water displaced by the body. Due to this stability of the body gets affected, so use the concept of buoyancy and characteristics of the floating body for the information about the metacenter.


Complete step by step solution
When the body floats in the liquid, it tends to push the liquid so the surrounding liquid also pushes the body in the upward direction with as much force as it can, and this upwards force is known as a buoyant force. Due to this force, the stability of the floating body gets affected and depends on the metacenter of the body. Whenever a body is floating in the liquid, it acquires a small amount of angular displacement, and it starts oscillating about some point of the body. This point about which the body starts to oscillate is called metacenter.

The floating body will acquire a stable equilibrium position when the metacenter of the body lies above the centre of gravity because, for the stable condition, the centre of gravity must be as low as possible.

Therefore, option (D) is correct that is above the center of gravity.

Note: For the stability of the completely submerged body, the center of gravity must be below the center of buoyancy, and for the stability of the floating body, the center of gravity must be below the metacenter of the body.