A cylindrical container has mass M and height H. the centre of mass of the empty container is at height (H)/(2) from the base. A liquid, when completley filled in the container, has mass (M)/(2) this liquid is poured in the empty contaienr. (a) How does the centre of mass of the system (container+liquid) move as the height (x) of liquid column changes from zero to H? Explain your answer qualitatively. Draw a graph showing the variation of height of centre of mass of the system (x_(cm)) with x. (b) Find the height of liquid column x for which the centre of mass is at its lowest position.

A cylindrical container has mass M and height H. the centre of mass of

1.	A cylindrical container has mass M and height H. the centre of mass of the empty container is at height (H)/(2) from the base. A liquid, when completley filled in the container, has mass (M)/(2) this liquid is poured in the empty contaienr. (a) How does the centre of mass of the system (container+liquid) move as the height (x) of liquid column changes from zero to H? Explain your answer qualitatively. Draw a graph showing the variation of height of centre of mass of the system (x_(cm)) with x. (b) Find the height of liquid column x for which the centre of mass is at its lowest position.
Answer» Answer :(a) The COM first FALLS attains a minimum HEIGHT and then it rises to original height `(H)/(2)` (b) `x=(SQRT(6)-2)H`