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 temperatures 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.

Answer 1

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Recall the concept of law of conservation of mass. As per this law, if there is no external force acting on the system, then the mass of the body remains constant over time. So it can never be created and nor be destroyed.

Complete step by step solution:
Step I:
Let the radius of the sphere before it breaks into parts is$R$
When the drop breaks into two parts, its radius is $r$
The total mass of the drop will remain the same before and after breaking into two parts. Suppose $\rho$is
the density of the droplets.

Step II:
It is known that $Density = \dfrac{{Mass}}{{Volume}}$
$Mass = Volume \times Density$

The water droplet is of the shape of a sphere. So formula of volume of sphere is $= \dfrac{4}{3}\pi {R^3}$

Step III:
As per law of conservation of mass,
Mass of droplet before breaking = Mass of droplet after breaking

$\rho \times \dfrac{4}{3}\pi {R^3} = 2 \times \rho \times \dfrac{4}{3}\pi {r^3}$
${R^3} = 2{r^3}$
$R = {(2)^{1/3}}r$
$\dfrac{R}{r} = {(2)^{1/3}}$
Squaring both sides of the above equation,
$\dfrac{{{R^2}}}{{{r^2}}} = {(2)^{2/3}}$

Step IV:
Since the mass of the system is constant, before and after the drop breaks. So the sum of the masses of the two droplets is equal to the original mass of the drop.

$\therefore$ Statement (b) is the right answer.

Note: It is to be noted that the term mass can be confused with the term weight. But they both are different terms. Mass is the quantity of matter contained in any body and it remains constant always. The shape of the system can change but its mass will always be the same. But weight is the force that attracts a body towards the centre of Earth. It changes from place to place.