# 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?

Given:

Mass of the object = m

Initial height of the object from earth’s centre = R

Final height of the object from earth’s centre = 2R

Let the mass of earth be M. We know that the gravitational potential energy of an object is given by,

Where r is the distance between the object and centre of earth. When the object is at its initial position it is at a distance of R from the centre of the earth. Then its potential energy,

When the object is raised to a height 2R, then the potential energy is given by,

Now the gain in gravitational potential energy is given by

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