A marble of mass `x` and diameter `2r` is gently released in a tall cylinder containing honey. If the marble displaces mass `y(ltx)`of the liquid, then the terminal velocity is proportional to

Options

A. `x+y`
B. `x-y`
C. `(x+y)/(r)`
D. `(x-y)/(r)`

Answer

D

Explanation

`v_(0)=(2)/(9)r^(2)((rho-rho^(1))g)/(eta),x=(4)/(3)pir^(3)rho(or)`
`rhoalpha=(x)/(r^(3)),rho^(1)alpha(y)/(r^(3)),v_(0)alpha(x-y)/(r)`