A hollow cylinder of height 100 cm and diameter 8 cm has its top end open. It contains water up to a height of 50 cm. Mass per square centimetre of the hollow cylinder is 9 g. Find the height of the centre of gravity of the water-cylinder system from the base of the cylinder.

A hollow cylinder of height 100 cm and diameter 8 cm has its top end o

1.	A hollow cylinder of height 100 cm and diameter 8 cm has its top end open. It contains water up to a height of 50 cm. Mass per square centimetre of the hollow cylinder is 9 g. Find the height of the centre of gravity of the water-cylinder system from the base of the cylinder.
Answer» Solution :Centre of gravity of the curved surface of the empty cylinder is 50 cm above its BASE at P Fig. Weight of the base of the empty cylinder `= PI(4)^(2)xx9xx "g dyn" ""` [g= acceleration due to gravity ] Weight of curved surface of the cylinder `=2pixx4xx100xx9xxg `dyn. Its centre of gravity is at `G_(1)` where `PG_(1)` = 50 cm. Weight of water in the cylinder `= pi(4)^(2)xx50xx1xxg` dyn and centre of gravity of this water is at `G_(2)` which is 25 cm above the base of the cylinder. Suppose the centre of mass of the cylinder filled with water is at G, which is h cm above its base. The centreof gravity COINCIDES with this centre of mass. Taking moments of all the weights about P, `2pixx4xx100xx9xxG_(1)P+pixx16xx50xx1xxG_(2)P` = `(pixx16xx9+2pixx4xx100xx9+pixx16xx50xx1)xxGP` or, `2pixx4xx100xx9xx50+pixx16xx50xx1xx25` =(`pixx16xx9+2pixx4xx100xx9+pixx16xx50xx1)xxh` or, h = 46.7 cm.