The velocity of small ball of mass `M` and density `d_(1)` when dropped a container filled with glycerine becomes constant after some time. If the density of glycerine is `d_(2)`, the viscous force acting on ball is

Options

A. `Mg(d_1-d_2)`
B. `Mg(1-(d_2)/(d_1))`
C. `Mgd_1d_2`
D. `Mg(d_1)/(d_2)`

Answer

C

Explanation

For the spherical ball falling in a liquid with terminal velocity v,
Downward force due to gravity
=Upthrust+Viscous force
`:." "4/3piR^3d_1g=4/3piR^3d_2g+`viscous froce (`6pinav`)
`:.` Viscous force (F)`=4/3piR^3(d_1-d_2)g`
`=4/3piR^3d_1(1-(d_2)/(d_1))g`
`:." "F=Mg(1-(d_2)/(d_1))`
Where Mg`=4/3piR^3d_1g`