## Question

A cylindrical piece of cork of height *h* and density ρ* _{c}* floats vertically in a liquid of density ρ

*. The cork is depressed slightly an released. If viscous effects are neglected, the time period of vertical oscillations of the cylinder is given by*

_{l}### Solution

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

#### SIMILAR QUESTIONS

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