A hollow plastic ornament consists of a thin spherical shell that completely encloses an air cavity. The shell has inner radius 5.0cm, outer radius 5.2cm, and uniform density 1.20gcm−3. The ornament is gently placed in a tub of fresh water (density 1.00gcm−3) and allowed to come to rest.
(a) Calculate the mass of the ornament.
(b) Determine the average density of the entire ornament (shell plus enclosed air).
(c) Based on your result in part (b), calculate the fraction of the ornament’s volume that remains below the waterline when it is floating in equilibrium.
(d) The ornament is to be painted uniformly on the outside. Determine the maximum additional mass of wet paint that can be applied before the ornament would no longer remain afloat.