$(1)$ An empty cylindrical bucket, $0\mathrm{.}3$ m in diameter and $0\mathrm{.}5$m long whose wall thickness and weight can beconsidered as negligible is forced with its open end firstinto water until its lower edge is $4$ m below the surface.What force will be required to maintain position,assuming the trapped air to remain at constanttemperature during the entire operation? Atmosphericpressure $=1\mathrm{.}03$ kg$/$cm$2.$