Q146 / 160 · AP EAMCET 2014 · Physics

When a big drop of water is formed from $n$ small drops of water, the energy loss is $3 E$, 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

  • A
    $\frac{4 R}{r^2}$
  • B
    $\frac{4 R}{r}$
  • C
    $\frac{2 R^2}{r}$
  • Correct answer
    D
    $\frac{4 R^2}{r^2}$

Solution

The energy of $n$ small drop - the energy of the bigger drop = Energy loss by bigger drop $$ \begin{gathered} n \times 4 \pi r^2 \times T-4 \pi r^2 \times T=3 \times 4 \pi R^2 \times T \\ n \times 4 \pi r^2 \times T=12 \pi R^2 \times T+4 \pi R^2 \times T \\ n=\frac{16 \pi R^2 \times T}{4 \pi r^2 \times T} \\ n=4 \frac{R^2}{r^2} \end{gathered} $$

Hence, the correct answer is option: 'D'.

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