Suppose a vertical tunnel is along the diameter of earth, assumed to be a sphere of uniform mass density \"d\". If a body of mass m is thrown in this tunnel, its acceleration at a distance y from the centre is --------------

consider a sphere of radius y inside the bigger sphere then ,

mass of this sphere is dm = d(4piy³/3)  ..........1                 (volume = 4pir³/3)

gravitational field due to this on its surface (E_y)= Gdm/y²

                                                            =4piGdy/3

now force on particle at a distance y is F_y = E_ym

                                                         =4piGdmy/3

        F = ma 

so accleration of particle (a_y)= 4pidGy/3

this is the required accleration

Approved