Question

A drop of water breaks into two droplets of equal size. In this process which of the following statements is correct ?
a) the sum of temperature of the two droplets together is equal to the original temperature of the drop.
b) the sum of masses of the two droplets is equal to the original mass of the drop.
c) the sum of the radii of the two droplets is equal to the radius of the original drop.
d) the sum of the surface areas of the two droplets is equal to the surface area of the original drop.

• A. a is correct
• B. b is correct
• C. c is correct
• D. d is correct

Answer 1

The correct option is B b is correct

When a drop of water breaks into two droplets, the total mass of the system remains the same, that is, sum of masses of the two droplets is equal to the mass of the original drop.

Hence $\rho \times \frac{4}{3}\pi R^3=2\times \rho \times \frac{4}{3}\pi r^3$

$⟹R=2^{1/3}r$

Hence the surface area is in the ratio $\frac{R^2}{r^2}=2^{2/3}$

Option B is correct.