Mechanical Properties Of Fluids Question 2
Question 2 - 2024 (01 Feb Shift 2)
A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :
(1) 100 times
(2) 10 times
(3) $\frac{1}{100} \mathrm{th}$
(4) $\frac{1}{10} \mathrm{th}$
Show Answer
Answer: (4)
Solution:
Lets say radius of small droplets is $r$ and that of big drop is $R$
$\frac{4}{3} \pi \mathrm{R}^{3}=1000 \frac{4}{3} \pi \mathrm{r}^{3}$
$\mathrm{R}=10 \mathrm{r}$
$\mathrm{U}_{\mathrm{i}}=1000\left(4 \pi \mathrm{r}^{2} \mathrm{~S}\right)$
$\mathrm{U}_{\mathrm{f}}=4 \pi \mathrm{R}^{2} \mathrm{~S}$
$=100\left(4 \pi \mathrm{r}^{2} \mathrm{~S}\right)$
$\mathrm{U}{\mathrm{f}}=\frac{1}{10} \mathrm{U}{\mathrm{i}}$
