Asmooth ball that has a diameter of 100 mm is dropped in a tank filled with oil of density 900 kg/m and dynamic viscosity 0.036 pa-s. the ball travels 70 cm in 2 seconds. if it is assumed that terminal speed has been reached. what is the density of the ball?

The density of the ball is 902.31

Explanation:

In order to determinate the density of the ball, under the assumption that terminal speed has been reached, Stoke's Law for terminal velocity can be used. But first we need to convert all units to SI units so we can find the terminal velocity.

Given information in SI units.

Diameter of the ball.

Radius of the ball.

Oil density.

Dynamic viscosity of the oil.

Distance traveled

Time

Finding the terminal velocity.

Under the assumption that the ball has reached terminal velocity in that time then the average velocity will give us the terminal velocity that is

Finding density of the ball.

The Stoke's law for terminal velocity of sphere falling in a fluid is given by

where is the density of the ball.

We can solve for it and we get

Getting the density in one side.

Replacing values we get

The density of the ball is 902.31

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