A satellite is orbiting just above the surface of a planet of average density `D` with period `T`. If `G` is the universal gravitational constant, the quantity `(3pi)/G` is equal to

Options

A. `T^(2)D`
B. `3piT^(2)D`
C. `3piD^(2)T`
D. `D^(2)T`

Answer

A

Explanation

Using `T=2pisqrt((R^(3))/(GM))=2pisqrt((R^(3))/(Gxx4/3piR^(3)D))`
`T^(2)=(4pi^(2)R^(3))/(G4/3piR^(3)D)=(3pi)/(DG)rArr (3pi)/G=T^(2)D`