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Class 11 NEET Physics Gravitation Questions
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© examsnet.com
Question : 15
Total: 83
A particle of mass '
m
' is projected with a velocity
v
=
k
V
e
(
k
<
1
)
from the surface of the earth.
(
V
e
=
escape velocity)
The maximum height above the surface reached by the particle is
[NEET 2021]
R
(
k
1
−
k
)
2
R
(
k
1
+
k
)
2
R
2
k
1
+
k
R
k
2
1
−
k
2
Validate
Solution:
👈: Video Solution
given
v
=
k
V
e
where,
k
<
1
Thus,
v
<
V
e
From conservation of mechanical energy,
1
2
m
v
2
−
G
m
M
R
=
−
G
m
M
(
R
+
h
)
⇒
v
2
2
=
G
M
R
−
(
G
M
)
(
R
+
h
)
=
h
R
(
R
+
h
)
G
M
⇒
1
2
k
2
V
e
2
=
G
M
h
R
(
R
+
h
)
We know,
V
e
=
√
2
G
M
R
⇒
1
2
k
2
(
2
G
M
R
)
=
G
M
h
R
(
R
+
h
)
k
2
=
h
(
R
+
h
)
R
k
2
+
h
k
2
=
h
R
k
2
=
h
(
1
−
k
2
)
∴
h
=
R
k
2
(
1
−
k
2
)
© examsnet.com
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