Suppose the gravitational force varies inversely as the (n^ th ) power of distance. Then the time period of a planet in circular orbit of radius (R ) around the sun will be proportional to

Step-by-step solution

Gravitational force, F 1 r^n F= k r^n where k is a constant. For a planet, moving in a circular orbit of radius R, F= k R^n But, F=m ^2 R aligned & k R^n =m R ( 2 T )^2 k R^ n+1 = m(2 )^2 T^2 & T^2 R^ n+1 & T R^ n+1 2 . aligned