MCQ
A big drop is formed by coalescing $1000$ small droplets of water. The ratio of surface energy of $1000$ droplets to that of energy of big drop is $\frac{10}{x}$. The value of $x$ is_______.
- A$5$
- B$8$
- ✓$1$
- D$3$
✓
Answer
Correct option: C.
$1$
c
$1000 \frac{4}{3} \pi \mathrm{r}^3=\frac{4}{3} \pi \mathrm{R}^3$
$1000 \frac{4}{3} \pi \mathrm{r}^3=\frac{4}{3} \pi \mathrm{R}^3$
$10 \mathrm{r}=\mathrm{R}$
$\mathrm{R}=10 \mathrm{r}$
$\frac{\text { S.E. of } 1000 \text { drops }}{\text { S.E. of Big drop }}=\frac{1000\left(4 \pi^2\right) T}{4 \pi R^2 T}$
$=\frac{1000 \times \mathrm{r}^2}{(10 \mathrm{r})^2}=10=\frac{10}{\mathrm{x}}$
$\therefore \quad \mathrm{x}=1$
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