if g is the acceleration due to gravity on the earth's surface , the gain in the potential energy of an object is mass m raised from the surface to a height equal to the radius R of the earth , is [AIEEE 2004]
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if g is the acceleration due to gravity on the earth's surface , the gain in the potential energy of an object is mass m raised from the surface to a height equal to the radius R of the earth , is [AIEEE 2004]
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Explanation:
Let M, R be the mass and radius of the earth. Then
g=GM/R
2
or GM=gR
2
(i)
Potential energy of the object on the surface of earth
U
1
=
R
−GMm
The potential energy of the object at a height equal to radius of the earth is
U
2
=
2R
−GMm
Gain in PE is
U
2
−U
1
=−
2R
GMm
+
R
GMm
=
2R
GMm
=
2R
(gR
2
)m
=
2
1
mgR.
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