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**:
The gravitational potential (V) at a distance r from the center of the Earth is given by:
\[ V = -E \times r \]

3. **Substitute the Known Values**:
Substitute the values of E and r into the formula:
\[ V = - (4.8 \, \text{N/kg}) \times (10^7 \, \text{m}) \]

4. **Calculate the Gravitational Potential**:
\[ V = - 4.8 \times 10^7 \, \text{J/kg} \]
Therefore, the gravitational potential at that point is:
\[ V = -4.8 \times 10^7 \, \text{J/kg} \]

### Final Answer:
The gravitational potential at the point 10,000 km from the center of the Earth is \(-4.8 \times 10^7 \, \text{J/kg}\).

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