A jar is filled with two types of balls, red and green. Red balls have radius $r_1$ and mass $m_1$, green balls have radius $r_2$ and mass $m_2$.
If initially the balls are randomly placed throughout the jar, and we are to shake this jar, generally one type of balls will tend to gather at the top. Why does this happen?
What are necessary conditions on $r_1$, $r_2$, $m_1$, $m_2$ such that green balls are more likely to occupy the upper part of the jar after shaking?