prove that the increase in gravitational
potential energy of a body of at a height h
near the earth surface is ∆u = mgh.
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ANSWER
If a point mass m is placed at a height h from surface of earth, the potential energy is
U
h
=−
(R+h)
GMm
=
R(1+
R
h
)
−gR
2
m
=
R
−gR
2
m
(1+
R
h
)
−1
(∵g=
R
2
GM
)
U
h
=
R
2
−gR
2
m(R−h)
=−gm(R−h)
⇒V=
m
U
h
=
m
−gm(R−h)
=−g(R−h
hope u got the answer ✋
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