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 sigma//rho`
B. `mg(1+sigma//rho)`
C. `mg(1-(sigma)/(rho))`
D. `mg`

Answer

C

Explanation

Let r be radius of drop, `:. V=(4)/(3)pi r^(3)`
When velocity of ball becomes constant, then forces are balance. So
Viscous force, `F=(4)/(3)pi r^(3) rho g - (4)/(3)pi r^(3) sigma g`
`=(4)/(3)pi r^(3) rho g(1-(sigma)/(rho))`
`=V rho g(1-(sigma)/(rho))` `[.: Vxxrho =m]`
`=mg(1-(sigma)/(rho))`