question_answer

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  Is t and its distance from the galaxy?s axis is r, then: JEE Main Online Paper (Held On 10 April 2015)

A) \[T\propto {{r}^{2}}\]                    

B) \[T\propto r\]

C) \[{{T}^{2}}\propto {{r}^{3}}\]                     

D) \[T\propto \sqrt{r}\]

Correct Answer: B

Solution :

                 \[F=\left( \frac{k}{r} \right)m\]k is some constant so \[\frac{m{{v}^{2}}}{r}=\frac{km}{r}\Rightarrow v=\]constant \[T=\frac{2\pi r}{v}\]                      \[T\propto r\]straight line