Problem 7: A small sphere of volume V falling in a viscous medium, acquire a terminal velocity v_T. What will be the terminal velocity of a sphere of the same material and volume 8 V falling through the same medium?

Answer

Given data   Volume of the first sphere = V

Terminal velocity of the first sphere = v_T

                               Volume of the second sphere = 8V

Required              Terminal velocity of the second sphere =?

Formula                          

Theory: Since volume is proportional to the cube of the radius. . Therefore, for an 8 fold increase in the volume, the radius of the sphere must increase by 2 fold. Therefore, if r is the radius of the small sphere and R is the volume of the big sphere, then, R = 2r. (Also see numerical problem 5 and MCQ 3).

Let’s suppose the radius of the small sphere = r Then the terminal velocity =

And terminal velocity of the big drop

This was required.