Question

Calculate the ** of small oscillations of a hydrometer (Fig. 4.2) which was slightly pushed down in the vertical direction. The mass of the hydrometer is m = 50 g, the radius of its tube is r = 3.2mm, the density of the liquid is p = 1.00g/cm3. The resistance of the liquid is assumed to be negligible.

Answer 1

If the hydrometer were in equilibrium or floating, its weight will be balanced by the buoyancy force acting on it by the fluid. during its small oscillation, let us locate the hydrometer when it is a vertically downward distance x from its equilibrium position. obviously the net unbalanced force on the hydrometer is the excess buoyancy force direction upward and equals πr2xρg. Hence for the hydrometer.