## Question

Eight spherical rain drops of the same mass and radius are falling down a terminal speed of 6 cms^{–1}. If they coalesce to form one big drop, what will be its terminal speed? Neglect the buoyancy due to air.

### Solution

24 cm s^{–1}

Let *r* be the radius of each small drop. The volume of each drop . Let *R* be the radius of the big drop formed when 8 small drops coalesce. The volume of the big drop will be 8 times that of the small drop. Hence

i.e., the radius of the big drop is twice the radius of each small drop. Now, if the buoyancy of the drop due to air is neglected, the terminal speed of the small drop is given by

The terminal speed of the big drop will be

Dividing (i) and (ii), we have

.

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