A design for a hydrometer in which the bottom part is a hollow cylinder with a $1\mathrm{.}00-$in diameter, and the top is a tube with a $0\mathrm{.}25-$in diameter. The empty hydrometer weighs $0\mathrm{.}020$ Ib$.($Note that this is for a specific gravity of $1\mathrm{.}00).$

$5\mathrm{.}14$ For the hydrometer designed in Problem $5\mathrm{.}13,$ what will be the specific gravity of the fluid in which the hydrometer would float at the top mark?