A metallic sphere of mass M falls through glycerine with a terminal velocity v. If we drop a ball of mass 8M of same metal into a column of glycerine, the terminal velocity of ball will be

Options

A. 2v
B. 4v
C. 8v
D. 16v

Answer

B

Explanation

Let r and R be the radii of sphere and ball respectively. Then
`M = (4)/(3) pi r^(3) rho and 8M = (4)/(3) pi R^(3) rho`
`:. R^(3) = 8r^(3) or R= 2r`
As `v prop r^(2)`
`:. (v.)/(v) = ((R )/(r ))^(2) = ((2r)/(r ))^(2) = 4 or v. = 4v`