Question

if the density of the is 2x 10^3 kg/m^3 ,density of steel is 8 x 10^2 kg/m^3 and coefficent of viscosity of oil is 2Ns/m^2 .What will be the constant velocity attained by the ball of radius 1mm?

Answer 1

Note #1: the data is changed, but the body of the answer has been sourced from another answer by me.

Note #2: the given data is incorrect, since with this data, the ball will not acquire a non-zero velocity, i.e., it will float on the liquid, with zero velocity. The particular data that seems wrong is the density of steel, given to be 800 kg/m^3, while the actual density is around 8000 kg/m^3. This solution uses the latter.

The formula for terminal velocity of a ball of radius r, of material of density , falling in a material of density , and coefficient of viscosity  is given by:

$v_{t} = \frac{2}{9} \frac{r^2 * (\rho_{s} - \rho_{l}) * g}{\eta}$

Substituting the given values, we get:

$v_{t} = 0.0067 m/s, or 0.67 cm/s, or \frac{2}{3} cm/s$

Note that the value of g is taken to be $10m/s^2$.

For the derivation of the initial formula, kindly refer to my answer to: https://brainly.in/question/8357895