Gravitational potential energy of body of mass `m` at a height of `h` above the surface of earth (M = mass of earth , R = radius of earth) is

Options

A. `(GMm)/(h)`
B. `(GMm)/((R+h))`
C. `(-GM)/((R+h))`
D. `-(GMm)/((R+h))`

Explanation

To find the gravitational potential energy (U) of a body of mass \( m \) at a height \( h \) above the surface of the Earth, we can use the formula for gravitational potential energy in the context of gravitational fields.

### Step-by-Step Solution:

1. **Understand the Gravitational Potential Energy Formula**:
The gravitational potential energy \( U \) of a mass \( m \) in a gravitational field created by a mass \( M \) (in this case, the Earth) at a distance \( r \) from the center of the mass \( M \) is given by the formula:
\[ U = -\frac{G M m}{r} \]
where \( G \) is the universal gravitational constant.

2. **Identify the Distance from the Center of the Earth**:
When the body is at a height \( h \) above the surface of the Earth, the distance \( r \) from the center of the Earth to the body is:
\[ r = R + h \]
where \( R \) is the radius of the Earth.

3. **Substitute \( r \) into the Potential Energy Formula**:
Substitute \( r = R + h \) into the gravitational potential energy formula:
\[ U = -\frac{G M m}{R + h} \]

4. **Final Expression**:
Thus, the gravitational potential energy of the body of mass \( m \) at a height \( h \) above the surface of the Earth is:
\[ U = -\frac{G M m}{R + h} \]

### Conclusion:
The gravitational potential energy of a body of mass \( m \) at a height \( h \) above the surface of the Earth is given by:
\[ U = -\frac{G M m}{R + h} \]