ANS:D - none of these.

The time of oscillation of a floating body is independent of the metacentric height. Here's an explanation: The time period of oscillation (T) of a floating body, such as a ship or a buoyant object, depends primarily on the moment of inertia of the body and the restoring torque (typically due to buoyancy). The metacentric height (GM) affects the stability of the floating body but does not directly influence the natural period of oscillation.

• Metacentric Height (GM): It is a measure of the initial static stability of a floating body. A higher metacentric height indicates greater stability against tilting.
• Time of Oscillation: This refers to the period it takes for the body to complete one full cycle of oscillation after being disturbed. It is primarily influenced by the shape, size, and mass distribution of the body (which determine its moment of inertia) and the buoyant forces acting on it.
• Buoyant Forces: These forces are crucial because they provide the restoring torque that brings the body back to its equilibrium position when it oscillates.

Therefore, the time of oscillation of a floating body is not directly affected by changes in the metacentric height. Instead, it depends on factors related to the body's inertia and the restoring forces (buoyancy) acting on it. Hence, the correct statement regarding the time of oscillation of a floating body is: independent of the metacentric height.