When a big drop of water is formed from n small drops of water, the energy loss is 3E, where, E is the energy of the bigger drop. If R is the radius of the bigger drop and r is the radius of the smaller drop then number of smaller drops (n) is?

Options

A. `(4R)/(r^(2))`
B. `(4R)/(r)`
C. `(2R^(2))/(r)`
D. `(4R^(2))/(r^(2))`

Answer

D

Explanation

Energy of n small drop - Energy of the bigger drop = Energy loss by bigger drop
`rArr n xx 4pi r^(2) xx S - 4pi R^(2) xx s = 3 xx 4pi R^(2) xx S`
`n xx 4pi r^(2) xx S = 12 pi R^(2) xx S + 4pi R^(2) xx S`
The number of smaller drops `n = (16 pi R^(2))/(4pi r^(2) xx S) = 4(R^(2))/(r^(2))`