At what height from the surface of earth the gravitation potential and the value of `g` are `- 5.4 xx 10^(7) J kg^(-2)` and `6.0 ms^(-2)` respectively ? Take the radius of earth as `6400 km`:

Options

A. `2000 km`
B. `2600 km`
C. `1600 km`
D. `1400 km`

Explanation

To solve the problem, we need to find the height \( h \) from the surface of the Earth where the gravitational potential \( V \) is \( -5.4 \times 10^7 \, \text{J/kg} \) and the value of \( g \) is \( 6.0 \, \text{m/s}^2 \). The radius of the Earth \( R_E \) is given as \( 6400 \, \text{km} \) or \( 6400 \times 10^3 \, \text{m} \).

### Step-by-Step Solution:

1. **Understanding Gravitational Potential and Gravitational Field:**
The gravitational potential \( V \) at a distance \( r \) from the center of the Earth is given by:
\[
V = -\frac{GM}{r}
...