The intensity of gravitational field at a point situated at a distance of 8000km form the centre of the earth is `6//kg`. The gravitational potential at that point is -(in joule /kg)

Options

A. `8xx10^(6)`
B. `2.4xx10^(3)`
C. `4.8xx10^(7)`
D. `6.4xx10^(14)`

Explanation

To find the gravitational potential at a point situated at a distance of 8000 km from the center of the Earth, given that the intensity of the gravitational field at that point is 6 N/kg, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formulas**:
- The intensity of the gravitational field (E) is given by the formula:
\[ E = \frac{G \cdot M_E}{r^2} \]
- The gravitational potential (V) is given by:
\[ V = -\frac{G \cdot M_E}{r} \]
Here, \( G \) is the gravitational constant, \( M_E \) is the mass of the Earth, and \( r \) is the distance from the center of the Earth.

2. **Relate the gravitational field and potential**:
- From the above formulas, we can express the relationship between gravitational field and potential:
\[ E = -\frac{dV}{dr} \]
- This implies that the gravitational potential can be calculated using the relationship:
\[ V = -E \cdot r \]

3. **Convert the distance from kilometers to meters**:
- The distance given is 8000 km. We need to convert this to meters:
\[ r = 8000 \text{ km} = 8000 \times 10^3 \text{ m} = 8 \times 10^6 \text{ m} \]

4. **Substitute the values into the potential formula**:
- Now, substituting the values of \( E \) and \( r \):
\[ V = -E \cdot r = -6 \, \text{N/kg} \cdot (8 \times 10^6 \, \text{m}) \]

5. **Calculate the gravitational potential**:
- Performing the multiplication:
\[ V = -6 \cdot 8 \times 10^6 = -48 \times 10^6 \, \text{J/kg} \]
- This can be simplified to:
\[ V = -4.8 \times 10^7 \, \text{J/kg} \]

6. **Final result**:
- The gravitational potential at the point is:
\[ V = -4.8 \times 10^7 \, \text{J/kg} \]