Question

A liquid drop of radius R breaks into 64 tiny drops each of radius r. If the surface tension of the liquid is T, then the gain in energy is

• A. $ 48\,\pi {{R}^{2}}T $
• B. $ 12\,\pi {{r}^{2}}T $
• C. $ 96\pi {{R}^{2}}T $
• D. $ 192\pi {{r}^{2}}T $

Answer 1

Answer: (D)

Volume of big drop = 64 $ \times $ volume of tiny drops or $ \frac{4}{3}\pi {{R}^{3}}=64\times \frac{4}{3}\pi {{r}^{3}} $ or $ R=4r $ So, the gain in surface energy = work done in splitting a liquid drop of radius R into n identical drops $ =4\pi T{{R}^{2}}({{n}^{1/3}}-1) $ $ =4\pi T\,{{(4r)}^{2}}({{64}^{1/3}}-1)=192\pi {{r}^{2}}T $