Question

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16 : 9. The ratio of their surface area is ______.

Options

• 4 : 3

• 64 : 27

• 16 : 9

• 9 : 16

Answer 1

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16 : 9. The ratio of their surface area is 16 : 9.

Explanation:

The terminal velocity of rain drop is

`"v"_"T" = (2(sigma - rho)"r"^2 "g")/(9 eta)`

`=> "v"_"T" prop "r"^2`   ...(i)

Also, surface area of rain drop, A = 4πr²

`=> "A" prop "r"^2`    ...(ii)

From Eqs. (i) and (ii), we get

`"A"_1/"A"_2 = "v"_("T"_1)/"v"_("T"_2)`

`= 16/9` or 16 : 9