Two rain drops reach the earth with different terminal velocities having ratio 9 : 4. Then, the ratio of their volumes is :-3 : 24 : 99 : 427 : 8

To find the ratio of the volumes of the two raindrops, we can use the relationship between terminal velocity and volume. The terminal velocity of an object is directly proportional to its volume.

Let's assume the terminal velocities of the two raindrops are 9v and 4v, where v is a constant. Since the terminal velocity is directly proportional to the volume, we can write:

Volume of first raindrop / Volume of second raindrop = (Terminal velocity of first raindrop / Terminal velocity of second raindrop)^3

Substituting the given values, we have:

Volume of first raindrop / Volume of second raindrop = (9v / 4v)^3

Simplifying this expression, we get:

Volume of first raindrop / Volume of second raindrop = (9/4)^3

Calculating the value of (9/4)^3, we find:

Volume of first raindrop / Volume of second raindrop = 729/64

Therefore, the ratio of the volumes of the two raindrops is 729 : 64.