InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
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)`.A. `R^(3//2)`B. `R^(3//5)`C. `R^(7//2)`D. `R^(7//2)` |
|
Answer» Correct Answer - D (d) According to the question, the gravitational force between the planet and the star is ` F prop (1)/(R^(5//2))` ` :. F=(GMm)/(R^(5//2))` where M and m be masses of star and planet respectively. For motion of a planet in a circular orbit, `mRomega^(2)=(GMm)/(R^(5//2))` `mR((2pi)/(T))^(2)=(GMm)/(R^(5//2))" " ( :. omega=(2pi)/(T))` `(4 pi^(2))/(T^(2))=(GM)/(R^(7//2)) implies T^(2)=(4 pi^(2))/(GM)R^(7//2)` `T^(2) prop R^(7//2) or T prop R^(7//4)` |
|