An object of mass `m` is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy ?

Explanation

To find the gain in potential energy when an object of mass \( m \) is raised from the surface of the Earth to a height equal to the radius of the Earth, we can follow these steps:

### Step 1: Define the Initial and Final Positions
- The initial position of the object is at the surface of the Earth, which is at a distance \( R \) (the radius of the Earth) from the center of the Earth.
- The final position of the object is at a height equal to the radius of the Earth, which means it is at a distance of \( 2R \) from the center of the Earth.

### Step 2: Calculate the Initial Potential Energy
The gravitational potential energy \( U \) at a distance \( r \) from the center of the Earth is given by the formula:
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