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

Options

A. 6
B. `4.8xx10^(7)`
C. `6xx10^(5)`
D. `4.8xx10^(2)`

Explanation

To find the gravitational potential at a point situated at a distance of 8000 km from the center of the Earth, we can use the relationship between gravitational intensity (I) and gravitational potential (V).

### Step-by-Step Solution:

1. **Identify the given values:**
- Gravitational intensity (I) = 6 N/kg
- Distance from the center of the Earth (R) = 8000 km = 8000 × 1000 m = 8,000,000 m = 8 × 10^6 m

2. **Use the relationship between gravitational intensity and gravitational potential:**
The gravitational potential (V) at a distance R from the center of the Earth can be calculated using the formula:
\[ V = -I \cdot R \]
Here, the negative sign indicates that gravitational potential is negative in a gravitational field.

3. **Substitute the values into the formula:**
\[ V = - (6 \, \text{N/kg}) \cdot (8 \times 10^6 \, \text{m}) \]

4. **Calculate the gravitational potential:**
\[ V = - (6 \cdot 8 \times 10^6) \, \text{J/kg} \]
\[ V = -48 \times 10^6 \, \text{J/kg} \]
\[ V = -4.8 \times 10^7 \, \text{J/kg} \]

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