Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of `6cms^(-1)`. If they coalesce to form one big drop, what will be its terminal speed? Neglect the buoyancy due to air

Answer

24

Explanation

Let r be the radius of each small drop and R that of the big drop. Since the volume remains the same,
` 8 xx ((4pi ) /(3) r ^ 3 ) = (4pi ) /(3 ) R ^3 rArr R = 2r `
Since terminal speed ` prop ` (radius ) `""^2` if the radius is doubled, the terminal speed becomes four times
` = 6 cm s ^(-1) xx 4 = 24 cm s ^(-1) `