# math

posted by
**Karl Haxell**
.

A perfectly cylindrical container standing upright with a top and bottom (an oil drum

or coke can for example) has an empty mass of M and a height of H. It is filled with

a liquid of uniform density of variable mass m up to height h. When the container is

full the centre of gravity is in the centre (H/2). As the container is emptied and m

reduces the centre of gravity moves down. Once the container is empty the centre

of gravity is again at the centre (height H/2). Using calculus calculate the value of h

in terms of H, m and M when the centre of gravity is at its lowest position.