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MHT CET · Physics · Mechanical Properties of Fluids

The change in energy when a big dropis split in sma \(\| n\) droplets is

  1. A \(4 R^{2}\left(n^{2 / 3}-1\right) I\)
  2. B \(4 \pi R^{2}\left(n^{1 / 3}-1\right) T\)
  3. C \(4 \pi R^{2}\left(n^{-1 / 3}-1\right) T\)
  4. D \(4 \pi R^{2}\left[n^{-2 / 3}-1\right] T\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(4 \pi R^{2}\left(n^{1 / 3}-1\right) T\)

Step-by-step Solution

Detailed explanation

When a drop of radius \(R\) split into \(n\) smaller drops (each of radius \(r\) ), then surface area of liquid increases. Hence, the work is to be done against surface tension. Since, the volume of liquid remains constant
\(
\begin{array}{l}
\therefore \quad \frac{4}{3} \pi R^{3}=n \frac{4}{3} \pi r^{3} \quad \therefore R^{3}=n r^{3} \\
\text { Work done }=T \times \Delta A \\
=T\left[n 4 \pi r^{2}-4 \pi R^{2}\right] \\
=4 \pi R^{2} T\left(n^{1 / 3}-1\right)
\end{array}
\)