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CGPET 2016 Solved Paper
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© examsnet.com
Question : 3
Total: 150
A very long (length
L
) cylindrical galaxy ismade of uniformly distributed mass and hasradius
R
(
R
<
<
L
)
. A star outside the galaxy isorbiting the galaxy in a plane perpendicularto the galaxy and passing through its center.If the time period of star is
T
and its distancefrom the galaxy’s axis is
r
, then
T
2
∞
r
3
T
∞
r
2
T
∞
r
T
∞
√
r
Validate
Solution:
Length of the galaxy
=
L
Mass is uni-formally distributed.
Distance of star from axis of galaxy
=
r
Star is orbiting the galaxy. So, centripetal force must equal to the force experience by gravitation of galaxy
∴
F
c
=
2
G
M
L
.
r
m
F
c
=
m
v
2
r
[
∵
v
=
ω
r
=
m
ω
2
r
]
m
ω
2
r
=
2
GMm
L
.
r
but,
ω
=
2
π
T
where,
T
=
time period
m
[
2
π
T
]
2
.
r
=
2
GMm
L
.
r
∴
T
∞
r
© examsnet.com
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