Jagaseesh was rotating a stone tied to an elastic rubber band. As time passes he kept on increasing its speed of rotation. As the speed increased, the length (i.e. radius) of the band was also increasing. His father Mr. Sridhar watched this and called Jagadeesh. When Jagadeesh came near by his father rotating the stone tied to the elastic band, he asked how this happened?
(i) State Keper's III law and give an expression.

Explanation

Jagadeesh father Mr. Sridhar explained this is related to Kepler's III law of planetary motion. He explained that time period of rotation of any object (say planets moving around sun) does not depend on the velocity of the object and radius of the circular path it means, whatever be the radius of the circular path or the velocity of the object, time period will not change at all. So you can measure the Time period of rotation of this stone too for different velocities (i.e. radius too is changing). Jagadeesh was surprised about his father's knowledge.
(i) Kepler's III lae states that "The square of the period of revolution of a planet around the sun is directly proportional to the cube of the mean distance between the planet and the sun.
`T^(2) prop r^(5)`
`(T^2)/(r^3)` = a constant.