Question

A floating body is said to be in stable equilibrium if its metacentre coincides with the centre of gravity.
(A) true
(B) false

Answer 1

The weight of the liquid displaced by the immersed part must be equal to the weight of the body. The centre of gravity and the centre of buoyancy of the body should be along the same vertical line. Then only the floating body is said to be in equilibrium.

Complete step-by-step solution:
Let us consider the body is floating in the water, due to the weight of the object some part of the object is displaced into the water. If the displaced weight of the object into the water is equal to the weight of the object which is not displaced. The centre of gravity lies vertically below the centre of buoyancy (stable equilibrium) and if centre of gravity lies Above the centre of buoyancy (unstable equilibrium).
When the body undergoes an angular displacement about a horizontal axis, the shape of the immersed volume changes and so the centre of buoyancy moves relative to the body. In fluid mechanics, the theoretical point at which an imaginary vertical line passing through the centre of buoyancy and centre of gravity intersects the imaginary vertical line through a new centre of buoyancy created when the body is displaced. A floating body is said to be in stable equilibrium if its metacentre lies above the centre of gravity.
Hence, the option (B) is the correct answer.

Note:- If the centre of gravity coincides with the metacentre, then the body is not in stable equilibrium. Then, the body experiencing some unstable movements. And then, the centre of gravity moves, it may lead to the twisting of the object in the water.