If M is the mass of the earth and R its radius, then ratio of the gravitational acceleration and the gravitational constant is

Options

A. `(R^(2))/(M)`
B. `(M)/(R^(2))`
C. `MR^(2)`
D. `(M)/(R)`

Explanation

To find the ratio of gravitational acceleration (g) to the gravitational constant (G), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Gravitational Acceleration (g)**:
The gravitational acceleration at the surface of the Earth can be expressed using the formula:
\[ g = \frac{GM}{R^2} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( R \) is the radius of the Earth.

2. **Setting Up the Ratio**:
We need to find the ratio of gravitational acceleration (g) to the gravitational constant (G):
\[ \text{Ratio} = \frac{g}{G} \]

3. **Substituting the Expression for g**:
Substitute the expression for \( g \) from the first step into the ratio:
\[ \text{Ratio} = \frac{\frac{GM}{R^2}}{G} \]

4. **Simplifying the Ratio**:
When we simplify the fraction, \( G \) in the numerator and denominator cancels out:
\[ \text{Ratio} = \frac{M}{R^2} \]

5. **Final Result**:
Therefore, the ratio of gravitational acceleration to the gravitational constant is:
\[ \frac{g}{G} = \frac{M}{R^2} \]