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State Stokes' law. The terminal veloci...

State Stokes' law.
The terminal velocity of copper ball of radius 2.0 mm falling through a tank of oil at `20^@ C` is 6.5 cm. `s^-1`.
Compute the coefficient of viscosity of the oil at `20^@ C` . (Density of oil is `1.5xx10^3 kg.m^-3` , density of copper is `8.9xx10^3 kg. m^-3`)

Text Solution

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1st part: N/A
2nd part: Terminal velocity of the ball, `v=6.5 cm . S^-1`
Radius of the ball , `r=2.0 mm= 2xx10^-3 m`
Density of oil , `sigma=1.5xx10^3 kg. m^-3`
Density of copper, `rho=8.9xx10^3 kg. m^-3`.
Acceleration due to gravity, `g=9.8m. s^-2`.
Hence, coefficient of viscosity of the oil,
`eta = 2/9. (r^2(rho-sigma)g)/(v)`
`=2/9.((2xx10^-3)^2(8.9-1.5)10^3xx9.8)/(6.5xx10^-2)`
`=0.99 kg. m^-1. s^-1`
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