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JEE Main Physics Class 11 Gravitation Part 1 Questions
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© examsnet.com
Question : 32
Total: 100
Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of smaller planet, the minimum firing speed needed is :
[6 Sep. 2020 (II)]
2
√
G
M
a
4
√
G
M
a
√
G
M
2
m
a
3
2
√
5
G
M
a
Validate
Solution:
Let A be the point where gravitation field of both planets cancel each other i.e. zero.
G
M
x
2
=
G
(
16
M
)
(
10
a
−
x
)
2
⇒
1
x
=
4
(
10
a
−
x
)
⇒
4
x
=
10
a
−
x
⇒
x
=
2
a
... (i)
Using conservation of energy, we have
−
G
M
m
8
a
−
G
(
16
M
)
m
2
a
+
K
E
=
−
G
M
m
2
a
−
G
(
16
M
)
m
8
a
K
E
=
G
M
m
[
1
8
a
+
16
2
a
−
1
2
a
−
16
8
a
]
⇒
K
E
=
G
M
m
[
1
+
64
−
4
−
16
8
a
]
⇒
1
2
m
v
2
=
G
M
m
[
45
8
a
]
⇒
v
=
√
90
G
M
8
a
⇒
v
=
3
2
√
5
G
M
a
© examsnet.com
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