A 500 kg polar bear of average density 950 kg/m3 is stranded on a melting chunk of ice in the ocean. The density of the sea water is 1030 kg/m3 and the density of the ice is 920 kg/m3.
(a) With reference to the forces involved, explain why the polar bear does not sink when standing on the ice.
(b) What is the smallest volume of ice that will keep the bear entirely above water?
(c) At some later time, the chunk of ice has shrunk to half its original volume. Will the bear still be able to keep its head above water without swimming? If so, calculate what volume of the bear remains above the surface.