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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 (Ey)= Gdm/y2
=4piGdy/3
now force on particle at a distance y is Fy = Eym
=4piGdmy/3
F = ma
so accleration of particle (ay)= 4pidGy/3
this is the required accleration
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