If the graviational potential at the surface of the earth is assumed to be zero, then the potential at infinity is given by

Options

A. 0
B. `prop`
C. `-(GM)/( R)`
D. `+(GM)/( R)`

Explanation

To solve the question, we need to find the gravitational potential at infinity when the gravitational potential at the surface of the Earth is assumed to be zero.

### Step-by-Step Solution:

1. **Understanding Gravitational Potential**:
The gravitational potential \( V \) at a distance \( r \) from a mass \( M \) is given by the formula:
\[ V = -\frac{GM}{r} \]
where \( G \) is the gravitational constant.

2. **Potential at the Surface of the Earth**:
Let \( M \) be the mass of the Earth and \( R \) be the radius of the Earth. The gravitational potential at the surface of the Earth (\( V_R \)) is:
\[ V_R = -\frac{GM}{R} \]
According to the question, we assume this potential to be zero:
\[ V_R = 0 \]

3. **Revising the Potential Scale**:
If we set \( V_R = 0 \), we can define a new potential scale. Let’s denote the new potential at the surface as \( V'_R \):
\[ V'_R = V_R + \frac{GM}{R} = 0 + \frac{GM}{R} = \frac{GM}{R} \]

4. **Potential at Infinity**:
The gravitational potential at infinity (\( V_{\infty} \)) in the original scale is:
\[ V_{\infty} = 0 \]
In the new scale, we denote this as \( V'_{\infty} \):
\[ V'_{\infty} = V_{\infty} + \frac{GM}{R} = 0 + \frac{GM}{R} = \frac{GM}{R} \]

5. **Final Result**:
Therefore, the potential at infinity in the new scale, where the potential at the surface of the Earth is zero, is:
\[ V'_{\infty} = \frac{GM}{R} \]

### Conclusion:
The gravitational potential at infinity, when the potential at the surface of the Earth is assumed to be zero, is given by:
\[ \frac{GM}{R} \]