Hydrometer

Calculate th eperiod of small oscillations of a hydrometer which was slightly pushed down in the vertical direction. The mass of the hydrometer is m=50g , the radius of its tube is r=3.2mm , the density of the liquuid is rho=1.00 g//cm^(3) . The rsistance of the liquid is assumed to be negligible.

A device used to measure the specific gravity of a liquid is called a hydrogmeter. In a simple hydrometer there is a cylindrical galss tube with some lead-weight at its bottom. The device floats in liquid while remaining vertical. The top part of the tube extends above the liquid and the divisions marked on the tube allows one to directly read the specific gravity of the liquid. The scale on the tube is calibrated such that in pure water it reads 1.0 at the water surface and a lenght z_(0) of the tube is submerged. calculate the specific gravity of the liquid if the liquid level is DeltaZ above the 1.0 mark. Disregard the curvature of the tube bottom.