Question

A small planet is revolving with a speed v around a very massive star in a circular orbit of radius r with a revolution period T. If the gravitational force between the planet and the star were inversely proportional to r, then,

• A. v is independent of r
• B. v decreases if r is increased.
• C. T increases if r is increased.
• D. T is independent of r.

Answer 1

Answer: (A), (C)

The correct options are
A

v is independent of r

C

T increases if r is increased.

F = $\frac{k}{r}$, k is constant.

$\frac{m{v}^2}{r}=\frac{k}{r}\Rightarrow v=\sqrt{\frac{k}{m}}$, which is independent of r.

$T=\frac{2\pi r}{v}=2\pi \sqrt{\frac{m}{k}}r\Rightarrow T\propto r$