# math

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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.

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