A planet is a homogeneous ball of radius R having mass M. It is surrounded by a dense atmosphere having density `rho=(sigma_(@))/(r)` where `simga_(@)` is a constant and r is distance from the centre of the planet. It is found that acceleration due to gravity is constant throughout the atmosphere of the planet. Find `simga_(@)`in terms of M and R.

Answer

`sigma_(0) =M/(2piR^(2))`