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JEE Advanced 2021 Paper 2
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© examsnet.com
Question : 18
Total: 57
The distance between two stars of masses
3
M
S
and
6
M
S
is
9
R
. Here
R
is the mean distance between the centers of the Earth and the Sun, and
M
S
is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period
n
T
, where
T
is the period of Earth's revolution around the Sun. The value of
n
is
Your Answer:
Validate
Solution:
The centre of mass lies at a distance
6
R
from lighter mass In circular orbit,
In circular orbit,
Time Period
T
=
2
π
√
R
3
G
M
S
Binary stars system
n
T
=
2
π
√
(
9
R
)
3
G
(
3
M
S
+
6
M
S
)
or,
n
×
2
π
√
R
3
G
M
S
=
9
×
2
π
√
R
3
G
M
S
[
∵
T
=
2
π
√
R
3
G
M
S
]
∴
n
=
9
© examsnet.com
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