A hydrometer is an instrument used to determine liquid density. A simple one is sketched in the figure below. The bulb of a syringe is squeezed and released to lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. (Assume the rod is cylindrical.) The rod, of length L and average density 0, floats partially immersed in the liquid of density . A length h of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by =
0L
L − h
.
(Do this on paper. Your instructor may ask you to turn in this work.)