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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 --------------

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 -------------- 

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

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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