Kepler's third law states that square of period of revolution (T) of a planet around the sun is proportional to third power of average distance r between sun and planet. That means `T^2 = Kr^3` here K is constant.
If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is `F = (GMm)/r^2` , here G is gravitational constant the relation between G and K is described as

Options

A. `GK = 4pi^2`
B. `GMK = 4pi^2`
C. `K=G`
D. `K = 1/G`

Answer

B

Explanation

`implies` Hint : `T = (2pi)/omega = (2pir)/v " " [ :. omega = v/r]`
`:. T = (2pir)/sqrt(GM) xxsqrtr " " [ :. v = sqrt((GM)/r)]`
`:. T = (2pi) / sqrt(GM) .r^(3/2)`
`:. T^(2)= (4pi^2)/(GM) .r^3`
comparing this equaotion with equation `T^2 =Kr^3`
`:. K = (4pi^2)/(GM)`
`:. GMK = 4pi^2)`