Question

If the radius of rain drop is doubled then kinetic energy gets increase by:

• A. \(24\) times
• B. \(10\) times
• C. \(16\) times
• D. \(2\) times

Hint:

Larger raindrops have much higher kinetic energy and therefore greater erosive power.

Answer 1

The Correct Option is C

Concept:
Kinetic energy of a raindrop depends on its mass and velocity. \[ KE=\frac{1}{2}mv^2 \]

Step 1: Relation of mass with radius.
A raindrop is approximately spherical. \[ \text{Volume}\propto r^3 \] Since mass is proportional to volume: \[ m\propto r^3 \]

Step 2: Effect of radius on kinetic energy.
In rainfall erosivity concepts, kinetic energy of rain drop is commonly related strongly to drop size. When radius is doubled, the kinetic energy increases by: \[ 2^4=16 \]

Step 3: Final answer. \[ \therefore \text{Correct Answer is (C)} \]