A perfectly cylindrical container standing upright with a top and bottom(an oil drum or coke can for example) of area A has an empty mass of M and a height of H.
It is filled with a liquid of uniform density(p)up to the height of h. When the container is full the centre of gravity is in the centre (H/”). As the container is emptied and h reduces the centre of gravity moves down. Once the container is empty the centre of gravity is again at the centre (height H/2)
1) Give an equation for the centre of gravity of the liquid in terms of p, A, h, H and M
2) Using Calculus calculate the value of h in terms of p, A, h, H and M when the centre of gravity is at its lowest position.
3) pROVE THAT THE VALUE OF H YOU HAVE CALCULATED GIVES THE LOWEST VALUE FOR THE CENTRE OF GRAVITY
4) Demonstrate that for this value of h it is the same as the height of the centre of gravity of the combined container and liquid
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