The ratio of energy required to raise a satellite to a height R from the surface of earth to the energy required to raise it to a height of 5R is
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Explanation:
Correct option is
C
2h:R
Energy required to raise a satellite upto a height h,
E
1
=ΔU=
1+
R
h
mgh
...(i)
E
2
= energy required to put in orbit
=
2
1
mv
0
2
=
2
1
m(
r
GM
) as v
0
= orbital speed
=
2
1
m(
R+h
GM
)=
2
1
m(
R
2
GM
)
1+
R
h
R
⇒E
2
=
2(1+
R
h
)
mgR
....(ii)
From equations (i) and (ii), we get
E
2
E
1
=
R
2h
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