A very long (length L ) cylindrical galaxy is made of uniformly distributed mass and has radius R ( R

Question

Quantrex Academy · Accepted Answer

Correct answer: B. T ∝ r

Due to a long solid cylinder gravitational field strength can be given as,

g = \dfrac{2G\lambda}{r}

Where,

\lambda =

linear mass density of galaxy.

For the orbital motion around the galaxy,

A very long (length L ) cylindrical galaxy is made of uniformly distributed mass and has radius R ( R

A very long (length L ) cylindrical galaxy is made of uniformly distributed mass and has radius R ( R

{f}_{g} = {f}_{centripetal}

⇒ mg = m{\omega}^{2}r

⇒ \dfrac{2G\lambda}{r} = {\omega}^{2}r

⇒ {\omega}^{2} ∝ \dfrac{1}{{r}^{2}}

⇒ \omega ∝ \dfrac{1}{r}

⇒ \dfrac{2\pi}{T} ∝ \dfrac{1}{r} ⇒ T ∝ r

So option

B

is correct.

A very long (length L ) cylindrical galaxy is made of uniformly...

Options

Correct answer

Step-by-step solution

More from Gravitation