If R is the radius of the earth and .g. the acceleration due to gravity, the mass of the earth is

Options

A. `(gR^2)/G`
B. `(gG)/R^2`
C. `(GR^2)/g`
D. `GgR^2`

Answer

To find the mass of the Earth using the given radius (R) and acceleration due to gravity (g), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for acceleration due to gravity**:
The acceleration due to gravity (g) at the surface of the Earth is given by the formula:
\[ g = \frac{G \cdot M}{R^2} \]
where:
- \( g \) is the acceleration due to gravity,
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( R \) is the radius of the Earth.

2. **Rearrange the formula to solve for the mass of the Earth (M)**:
To find the mass \( M \), we can rearrange the formula:
\[ M = \frac{g \cdot R^2}{G} \]

3. **Substituting the variables**:
Here, we substitute \( R \) with the radius of the Earth and \( g \) with the acceleration due to gravity at the surface of the Earth.

4. **Final expression for the mass of the Earth**:
Thus, the mass of the Earth can be expressed as:
\[ M = \frac{g \cdot R^2}{G} \]
This is the final formula for calculating the mass of the Earth based on its radius and the acceleration due to gravity.

### Final Answer:
\[ M = \frac{g \cdot R^2}{G} \]