A very crude model of a typical comet nucleus is a cube of ice (density \(1000
\mathrm{~kg} / \mathrm{m}^{3}\) ) \(10 \mathrm{~km}\) on a side. (a) What is the
mass of this nucleus? (b) Suppose \(1 \%\) of the mass of the nucleus evaporates
away to form the comet's tail. Suppose further that the tail is 100 million
\(\left(10^{8}\right) \mathrm{km}\) long and 1 million \(\left(10^{6}\right)
\mathrm{km}\) wide. Estimate the average density of the tail (in \(\mathrm{kg} /
\mathrm{m}^{3}\) ). For comparison, the density of the air you breathe is about
\(1.2 \mathrm{~kg} / \mathrm{m}^{3}\). (c) In 1910 the Earth actually passed
through the tail of Comet Halley. At the time there was some concern among the
general public that this could have deleterious effects on human health. Was
this concern justified? Why or why not?