Question 70: Properties of Matter

Question

A small liquid drop of radius $$R$$ is divided into 27 identical liquid drops. If the surface tension is $$T$$, then the work done in the process will be:

Accepted Answer

Volume constant
$$\begin{aligned}
& \frac{4}{3} \pi R^3=27 	imes \frac{4}{3} 	imes \pi r^3 \
& R^3=27 r^3 \
& R=3 r \
& r=\frac{R}{3} \
& r^2=\frac{R^2}{9}
\end{aligned}$$
$$\begin{aligned}
& 	ext { Work done }=T . \Delta A \
& =27 T\left(4 \pi r^2ight)-T 4 \pi R^2 \
& =27 T 4 \pi \frac{R^2}{9}-4 \pi R^2 T \
& =8 \pi R^2 T
\end{aligned}$$

Answer

$$4 \pi \mathrm{R}^2 \mathrm{~T}$$

Answer

$$8 \pi R^2 \mathrm{~T}$$

Answer

$$\frac{1}{8} \pi R^2 T$$

Answer

$$3 \pi R^2 \mathrm{~T}$$

Properties of Matter

A small liquid drop of radius $R is divided into 27 identical liquid drops. If the surface tension is T$, then the work done in the process will be:

Choose the correct answer: