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JEE Main Physics Class 11 Gravitation Part 1 Questions
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© examsnet.com
Question : 74
Total: 100
Two hypothetical planets of masses
m
1
and
m
2
are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is 'd'?
(Speed of
m
1
is
v
1
and that of
m
2
is
v
2
)
[Online April 12, 2014]
v
1
=
v
2
v
1
=
m
2
√
2
G
d
(
m
1
+
m
2
)
v
2
=
m
1
√
2
G
d
(
m
1
+
m
2
)
v
1
=
m
1
√
2
G
d
(
m
1
+
m
2
)
v
2
=
m
2
√
2
G
d
(
m
1
+
m
2
)
v
1
=
m
2
√
2
G
m
1
v
2
=
m
2
√
2
G
m
2
Validate
Solution:
We choose reference point, infinity, where total energy of the system is zero.
So, initial energy of the system = 0
Final energy
=
1
2
m
1
v
1
2
+
1
2
m
2
v
2
2
−
G
m
1
m
2
d
From conservation of energy,
Initial energy = Final energy
∴
0
=
1
2
m
1
v
1
2
+
1
2
m
2
v
2
2
−
G
m
1
m
2
d
or
1
2
m
1
v
1
2
+
1
2
m
1
v
2
2
=
G
m
1
m
2
d
...(1)
By conservation of linear momentum
m
1
v
1
+
m
2
v
2
=
0
or
v
1
v
2
=
−
m
2
m
1
⇒
v
2
=
−
m
1
m
2
v
1
Putting value of
v
2
in equation (1), we get
m
1
v
1
2
+
m
2
(
−
m
1
v
1
m
2
)
2
=
2
G
m
1
m
2
d
m
1
m
2
v
1
2
+
m
1
2
v
1
2
m
2
=
2
G
m
1
m
2
d
v
1
=
√
2
G
m
2
2
d
(
m
1
+
m
2
)
=
m
2
√
2
G
d
(
m
1
+
m
2
)
Similarly
v
2
=
−
m
1
√
2
G
d
(
m
1
+
m
2
)
© examsnet.com
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