If the density of the earth is doubled keeping its radius constant, then the new value of force of attraction on an object on the surface of the earth is how many times that in the previous case?

Explanation

To solve the question, we need to analyze how the force of attraction changes when the density of the Earth is doubled while keeping its radius constant. We will use the formula for gravitational force and the relationship between mass, volume, and density.

### Step-by-Step Solution:

1. **Understanding Gravitational Force**:
The gravitational force \( F \) acting on an object of mass \( m \) at the surface of the Earth is given by the formula:
\[
F = \frac{G \cdot M \cdot m}{r^2}
...