Twenty seven droplets of water each of radius $0.1 \mathrm{~mm}$ merge to form a single drop then the energy…

Twenty seven droplets of water each of radius $0.1 \mathrm{~mm}$ merge to form a single drop then the energy released is
  1. $1.6 \times 10^{-3} \mathrm{~J}$
  2. $1.6 \mathrm{~J}$
  3. $1600 \mathrm{~J}$
  4. $1.6 \times 10^{-7} \mathrm{~J}$

Solution

From $\begin{aligned} & \mathrm{W}=4 \pi \mathrm{r}^2 \mathrm{~T}\left(\mathrm{n}-\mathrm{n}^{2 / 3}\right) \\ & \mathrm{W}=4 \pi \times\left(0.1 \times 10^{-3}\right)^2 \times 0.072\left[27-(3)^{2 / 3}\right] \\ & =1.627 \times 10^{-7} \quad\left(\mathrm{~T}_{\text {water }}=0.075 \mathrm{~N} / \mathrm{m}\right) \end{aligned}$ /

Asked in: MHT CET 2023 (13 May Shift 1)

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