what will be the change in P.E. of a body of mass m when it is raised from height are above the Earth's surface to 5 by 2 are above the Earth surface?Re and Me are the radius and mass of the earth
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Answer:
Gravitational potential energy at any point at a distance r from the centre of the earth is U=−
r
GM
E
m
where M
E
and m be masses of earth and body respectively. At the surface of the earth, r=R
E
∴U
1
=−
R
E
GM
E
m
At a height h from the surface, r=R
E
+h=R
E
+nR
E
=(1+n)R
E
∴U
2
=−
(n+1)R
E
GM
E
m
change in potential energy is ΔU=U
2
−U1
=−
(n+1)R
E
GM
E
m
−(−
R
E
GM
E
m
)
=
R
E
GM
E
m
(1−
(n+1)
1
)=
(n+1)R
E
GM
E
mn
=mgR
E
(n+1)
n
(∵g=
R
E
2
GM
E
)
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