**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).

Letâ€™s suppose the radius of the
small sphere = r
Then the terminal
velocity =

And terminal velocity of the big drop

This was required.

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