The density inside a solid sphere of radius a is given by `rho=rho_0/r`, where `rho_0` is the density at the surface and r denotes the distance from the centre. Find the gravitational field due to this sphere at a distance 2a from its centre.

Answer

A, B

Explanation

Volume of small strip `dV = (4 pi r^(2)) dr` mass of this strip `dm = (rho) (dV)`

`= ((rho_(o)a)/(r)) (4 pi r^(2)) dr = (4pi a rho_(0)) (rdr)`
`:.` Mass of whole sphare `= int_(0)^(a) (4 pi a rho_(0)) rdr`
`m = (2 pi a^(3) rho_(0))`
`E = (GM)/((2a)^(2)) = (G(2 pi a^(3) rho_(0)))/(4a^(2))`
`= (pi G rho_(0) a)/(2)`