The velocity of a small ball of mass M and density d when dropped in a container filled with glycerine becomes constant after sometime. If the density of glycerine is 'd/2' then the viscous force acting on the ball will be

Options

A. Mg
B. `3/2 Mg`
C. 2 Mg
D. `(Mg)/(2)`

Answer

D

Explanation

`F_("net")=0`
`F_V+F_b=Mg`
`implies F_V=Mg-F_b`
`=4/3 pi R^3 dg-4/3 pi R^3 d/2 g=4/3 pi R^3 dg(1-1/2)`
`=4/3 pi R^3dg(1/2)=(Mg)/(2)`