The terminal velocity of a copper ball of radius 1.0 mm falling through a tank of oil at `20^(@)C` is `8.5cms^(-1)` .Compute the viscosity of the oil at `20^(@)C` .Density of oil is `1.5xx10^(3)kgm^(-3)` , density of copper is `8.9xx10^(3)kgm^(-3)`

Explanation

Radius of copper ball ,
`r=2.0mm=2xx10^(-3)m`
The terminal velocity of ball ,
`v_(t)=6.5cms^(-1)=6.5xx10^(-2)ms^(-1)`
Density of oil `sigma=1.5xx10^(3)kgm^(-3)`
Density of copper `rho=8.9xx10^(3)kgm^(-3)`
From Stoke.s law ,
`eta=(2)/(9)xx(r^(2)g)/(v_(t))(rho-sigma)`
`=(2xx(2xx10^(-3))^(2)xx9.8(8.9xx10^(3)-1.5xx10^(3)))/(9xx6.5xx10^(-2))`
`=9.917xx10^(-6+3+2)`
`=9.9xx10^(-1)`
`=0.99kgm^(9-1)s^(-1)`