Gravitational potential difference
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The work done in moving a unit mass from one point to another in a gravitational field is called gravitational potential difference. The SI unit is JKg
-1.
Gravitational potential energy
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Let a body of mass m be at a distance r from a body of mass M. The gravitational potential energy of the mass m is defined as the work done in bringing it from infinity to that point.
The work done in moving the mass m through a small distance dr in the gravitational field of M is,
dw = F dr
The total work done in bringing mass m from infinity to that point, is
Gravitational potential energy
Relation between gravitational field intensity and gravitational potential difference
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If M is the mass of a body around which a field exists and m is the test mass placed at a distance r from M in this field then,
Potential energy per unit mass is gravitational potential (V)
Gravitational potential energy of a mass m at a height h above the surface of the Earth
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The potential energy of a mass m at a height h is given by the expression
Considering P.E. at the surface of the Earth to be nil.
