Question

Several spherical drops of a liquid of radius r coalesce to form a single drop of radius R. If T is surface tension and V is volume under consideration, then the release of energy is

• A. $3VT\left( \frac{1}{r} + \frac{1}{R} \right)$
• B. $3VT\left( \frac{1}{r} - \frac{1}{R} \right)$
• C. $VT\left( \frac{1}{r} - \frac{1}{R} \right)$
• D. $VT\left( \frac{1}{r^{2}} + \frac{1}{R^{2}} \right)$

Answer 1

Answer: (B)

$3VT\left( \frac{1}{r} - \frac{1}{R} \right)$

Answer 2

Energy released = $4\pi TR^{3}\left\lbrack \frac{1}{r} - \frac{1}{R} \right\rbrack = 3\left( \frac{4}{3}\pi R^{3} \right)T\left\lbrack \frac{1}{r} - \frac{1}{R} \right\rbrack = 3VT\left\lbrack \frac{1}{r} - \frac{1}{R} \right\rbrack$