Question

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. if the gravitational force of attraction between the planet and the star is proportational to R^(-5//2), then (a) T^(2) is proportional to R^(2) (b) T^(2) is proportional to R^(7//2) (c) T^(2) is proportional to R^(3//3) (d) T^(2) is proportional to R^(3.75).

Answer 1

T² is proportional to:

• Given, F is proportional to $r^{-2.5}$

                    $\frac{mv^2}{r}$ is proportional to $r^{-2.5}$

                     v² is proportional to $r^{-2.5+ 1}$ = $r^{-1.5}$

• v is proportional to $r^{-0.75}$

• Time period of revolution, T is proportional to $\frac{r}{v}$

         Putting value of v,         ⇒ T is proportional to $\frac{r}{r^{-0.75}} = r^{1.75}$

• So, T² is proportional to $r^{1.75*2} = r^{3.5}$

• Option B is the correct answer.

Answer 2

Answer:

universal law of gravitational

mv^/R=G mn/R^5/2

option B is correct