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A very long (length L) cylindrical galax...

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R `(R lt lt L)` A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy's axis is r, then-

A

`Tpropsqrt(r)`

B

`Tpropr`

C

`Tpropr^(2)`

D

`T^(2)propr^(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(2M)/(Lx).(Gm)/(r)=mromega^(2)=mr(4pi^(2))/(T^(2))`
`T^(2)propr^(2)impliesTalphar`
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