Question
Show that the gravitational potential due to the earth at a height h from the surface of the earth is
Solution
Gravitational potential at any point is defined as the amount of work done in moving a unit mass from infinity to that point.
Mass, m = 1 kg
Let a unit mass be placed at P at a distance r from the centre of the earth.
The force acting on unit mass is,
If unit mass is moved by a distance dr towards O, then work done by gravitational force is,
Total work done when the unit mass is moved from infinity to a distance R + h from the centre is,
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This work done by definition is equal to gravitational potential.
∴
Hence, the result.
Mass, m = 1 kg
Let a unit mass be placed at P at a distance r from the centre of the earth.
The force acting on unit mass is,
If unit mass is moved by a distance dr towards O, then work done by gravitational force is,
Total work done when the unit mass is moved from infinity to a distance R + h from the centre is,
This work done by definition is equal to gravitational potential.
∴
Hence, the result.
