Mechanical Properties Of Fluids Question 7
Question 7 - 2024 (29 Jan Shift 2)
A small liquid drop of radius $\mathrm{R}$ is divided into 27 identical liquid drops. If the surface tension is $\mathrm{T}$, then the work done in the process will be :
(1) $8 \pi R^{2} \mathrm{~T}$
(2) $3 \pi R^{2} \mathrm{~T}$
(3) $\frac{1}{8} \pi R^{2} T$
(4) $4 \pi R^{2} \mathrm{~T}$
Show Answer
Answer: (1)
Solution:
Volume constant
$\frac{4}{3} \pi R^{3}=27 \times \frac{4}{3} \times \pi r^{3}$
$R^{3}=27 r^{3}$
$R=3 r$
$r=\frac{R}{3}$
$r^{2}=\frac{R^{2}}{9}$
Work done $=\mathrm{T} \cdot \Delta \mathrm{A}$
$=27 \mathrm{~T}\left(4 \pi \mathrm{r}^{2}\right)-\mathrm{T} 4 \pi \mathrm{R}^{2}$
$=27 \mathrm{~T} 4 \pi \frac{\mathrm{R}^{2}}{9}-4 \pi \mathrm{R}^{2} \mathrm{~T}$
$=8 \pi \mathrm{R}^{2} \mathrm{~T}$
