Question

A very long (length $L$) cylindrical galaxy is made of uniformly distributed mass and has radius $R(R<<L)$. A star outside 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. $T^2\propto r^3$
• B. $T\propto r$
• C. $T\propto r^2$
• D. $T\propto \sqrt{r}$

Answer 1

The correct option is B $T\propto r$

As given,

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

Where in $T=\frac{circumferenceoforbit}{orbitalvelocity}$

$F=\frac{2GMm}{L/r};F=\left(\frac{k}{v}m\right)$

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

$\therefore T\propto r$