﻿ A cylindrical piece of cork of height h and density ρc floats vertically in a liquid of density ρl. The cork is depressed slightly an released. If viscous effects are neglected, the time period of vertical oscillations of the cylinder is given by : Kaysons Education

# A Cylindrical Piece Of Cork Of Height h and Density ρc floats Vertically In A Liquid Of Density ρl. The Cork Is Depressed Slightly An Released. If Viscous Effects Are Neglected, The Time Period Of Vertical Oscillations Of The Cylinder Is Given By

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Let A be the cross-sectional area of the cork and M its mass. Figure (a) shows the static equilibrium, the weight of the cork being balanced by the weight of the liquid is displaces. If the cork is depressed through a distance x, as shown in fig (b), the buoyant force on it increases by  because  is the mass of the liquid displaced by dipping, g being the acceleration due to gravity. If viscous effects are neglected, the restoring force on the cork is given by

Where  Since  the

motion of the cork as simple

harmonic. The time period of the

motion is

Where M is the mass of the cork

Hence

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