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

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

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$\frac{4 R}{r}$

$\frac{4 R}{r^{2}}$

$\frac{4 R^{2}}{r^{2}}$

$\frac{2 R^{2}}{r}$

answer is C.

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Detailed Solution

$\begin{array}{l} ΔE = 3 E; 4 πT [{nr}^{2} - R^{2}] = 3 [4 {πR}^{2} T] \\ {nr}^{2} - R^{2} = 3 R^{2} \Rightarrow {nr}^{2} = 4 R^{2} \Rightarrow n = \frac{4 R^{2}}{r^{2}} \end{array}$