# A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R<<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 galaxys axis is r, then : Option 1)   Option 2) Option 3) Option 4)

As we learnt in

Time period of satellite -

$T=2\pi\sqrt{\frac{r^{3}}{GM}}$

$r=$ radius of orbit

$T\rightarrow$ Time period

$M\rightarrow$ Mass of planet

- wherein

$T=\frac{Circumference\: of\: orbit}{orbital\: velocity}$

$F=\frac{2GM}{Lr}m,$                $F=(\frac{k}{r})m,$

Here K is some constant

$(\frac{mv^2}{r})=\frac{km}{r}\Rightarrow v=\:constant$

$T=\frac{2\pi r}{v}$

$\therefore T\propto r$

Option 1)

Incorrect

Option 2)

Incorrect

Option 3)

Correct

Option 4)

Incorrect

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