$2\mathrm{.}86$ The plug and empty cylinder shown in Fig. P$2\mathrm{.}86$ weigh $1500$ lb $.$ Calculate the height $h$ needed to lift the plug if the radius $R$ of the $10-$ft$-$long cylinder is:

$($a$)12$ in$.$

$($b$)16$ in$.$

$($c$)20$ in $.$