## Question

The mass of the earth is and its radius is m. How much work will be done in taking a 10-kg body from the surface of the earth to infinity? What will be the gravitational potential energy of the body on the earth’s surface? If this body falls from infinity to the earth, what will be its velocity when striking the earth?

### Solution

The work done in taking a body of mass m from the surface of the earth to infinite is

Where *M _{e}* is the mass of the earth and

*R*its radius. Putting the values:

_{e}

The gravitational potential energy at the earth’s surface is

The work done in taking the body from the earth to infinity will be obtained in the form of kinetic energy when the body falls back on the earth. Hence if the body strikes the earth with a velocity *v*, then

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