Estimate the speed of vertically falling rain drops from the following data. Radius of the drops=0.02cm, viscosity of air `=1.8xx10^-4 poise, g=9.9ms^-2 and ` density of water `=1000 kg m^-3`.

Answer

A

Explanation

`r=0.02cm=2x10^-4m`
eta=1.8xx10^-4poise`
`=1.8xx10^-5decapoise`
`g=9.9m/s^2`
rho=1000kg/m^3`
To find terminal velocity of rain drops the force acting on the drops are
i the weight `(4/3)pir^3 rho g` downward.
ii Force of buoyancy `(4/3)pir^3 sigma g` upward.
iii Force of viscosity `6pieta rv` upward.
Because sigma of air is very smalll the force of buoyancy may be neglected.
Thus `6pieta rv=(4/3)pir^3rho g`
`=or v=2r^2(rhog)/(9eta)`
`=2xx(0.02xx10^-2)xx1000xx(9.9)/9xx(1.8xx10^-5)`
`=5m/sec`.