The gravitational field intensity at a point `10,000km` from the centre of the earth is `4.8Nkg^(-1)`. The gravitational potential at that point is

Options

A. `-4.8xx10^(7)Jkg^(-1)`
B. `-2.4xx10^(7)Jkg^(-1)`
C. `4.8xx10^(6)Jkg^(-1)`
D. `3.6xx10^(6)Jkg^(-1)`

Explanation

To find the gravitational potential at a point 10,000 km from the center of the Earth, we can use the relationship between gravitational field intensity (E) and gravitational potential (V).

### Step-by-Step Solution:

1. **Identify the given values:**
- Gravitational field intensity (E) = 4.8 N/kg
- Distance from the center of the Earth (r) = 10,000 km = 10,000 × 10^3 m = 10^7 m

2. **Recall the formula for gravitational potential (V):**
The gravitational potential (V) at a distance r from the center of the Earth is given by:
\[ V = -E \cdot r \]

3. **Substitute the values into the formula:**
\[ V = - (4.8 \, \text{N/kg}) \cdot (10^7 \, \text{m}) \]

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

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