Keeping mass unchanged if radius of the earth increases by a factor 4, then by which factor density must have to be changed so that the value of g remains same ?

Explanation

To solve the problem, we need to determine how the density of the Earth must change if the radius increases by a factor of 4 while keeping the mass unchanged, so that the acceleration due to gravity (g) remains constant.

### Step-by-Step Solution:

1. **Understand the Formula for g**:
The acceleration due to gravity (g) at the surface of the Earth is given by the formula:
\[
g = \frac{G \cdot M}{R^2}
...