A laboratory stores two seemingly identical cylindrical containers, each sealed and opaque.
• Container X is known to be filled entirely with a liquid of uniform density 1.1×103kgm−3.
• Container Y has the same external dimensions as Container X but consists of a solid plastic shell (density 950kgm−3) enclosing an inner cavity that is completely filled with the same liquid as in Container X.
When held in the hands, many students report that Container Y "feels lighter" even though both contain the same liquid.
Answer the following questions about the situation.
(a) State, in words, the physical meaning of the density of a substance and identify the quantities required to determine it.
(b) Without performing numerical calculations, explain qualitatively why Container Y can have a smaller overall mass than Container X even though it holds the same liquid. In your explanation, refer explicitly to the relative contributions of the shell and the liquid to the overall mass and volume of Container Y.
(c) Suppose the manufacturer wishes Container Y to have the same overall density as Container X. Describe one change to the design or materials of Container Y that would accomplish this goal and justify your answer in terms of mass–volume considerations.