A body of mass m is taken from Earth's surface to the height equal to half of radius of Earth . The increase in potential energy will be ?
1. mgR
2. 1/3 mgR
3. 3mgR
4. 1/4 mgR
1. mgR
2. 1/3 mgR
3. 3mgR
4. 1/4 mgR
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Answer:
mgRe/2
Explanation:
The gravitational potential energy at a height h is
U
h
=
R
e
+h
−GM
e
m
If h=R
e
⇒U
h
=
+2R
e
−GM
e
m
=
2
−mgR
e
& the gravitational potential energy on the surface of earth is
U
s
=
R
e
−GM
e
m
So change in potential energy △U=U
h
−U
s
=
2R
e
−GM
e
m
+
R
e
GM
e
m
=
2R
e
GM
e
m
△U=
2
mgR
e
It means that to move a body of a mass m from the surface of earth to a height h=R
e
, the energy required is
2R
e
GM
e
m
=
2
mgR
e