JEE Rotational
A binary star consists of two stars A (mass 2 . 2 Ms) and B (mass 1 1 Ms), where Ms is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is...
The answer is 6.
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2 solutions
Let xd be the distance of 2.2 from center of mass and (1-x)d that of 11. Angler velocity =
ω
same for both.
Since moments about mass center are equal, 2.2 * xd=11 * (1-x)d.......So x=5/6, and 1-x=1/6.
∴
B
m
o
m
e
n
t
u
m
=
(
6
d
)
2
∗
1
1
∗
ω
.
∴
A
m
o
m
e
n
t
u
m
=
(
6
5
d
)
2
∗
2
.
2
∗
ω
.
∴
r
e
q
u
i
r
e
d
r
a
t
i
o
=
(
6
d
)
2
∗
1
1
∗
ω
(
6
d
)
2
∗
1
1
∗
ω
+
(
6
5
d
)
2
∗
2
.
2
∗
ω
=
6
.
A nice problem..
Angular momentum of a body revolving with an angular velocity w = m ∗ r 2 ∗ w
Since they are revolving around a fixed center of mass, their angular velocity must be same. Thus, A n g u l a r m o m e n t u m o f B A n g u l a r m o m e n t u m o f t o t a l s y s t e m = m 2 ∗ r 2 2 m 1 ∗ r 1 2 + m 2 ∗ r 2 2
= m 2 ∗ r 2 2 m 1 ∗ r 1 2 + 1
= 6