A small planet is revolving around a very massive star in a circular orbit of radius ' R ' with a period of revolution ' T '. If the gravitational force between the planet and the star were proportional to ' R ^ -5 / 2 , then ' T ', would be proportional to

Step-by-step solution

For the planet to orbit around the star, the centripetal force must be provided by gravitational force. Hence, F _ G = F _ a F _ a - R ^ -5 / 2 ....(Given) Here, -ve sign indicates force is towards the centre of orbit. array ll & a - R ^ -5 / 2 & - ^2 R - R ^ -5 / 2 & ^2 R ^ -(5+2) / 2 & 4 ^2 ~T ^2 R ^ -7 / 2 & ~T ^2 R ^ 7 / 2 & ~T R ^ 7 / 4 array