If a hollow rod is passed through the centre of gravity of the earth and if a ball is passed - Physics - Laws Of Motion

Question

If a hollow rod is passed through the centre of gravity of the
earth and if a ball is passed into that hollow rod then what
happens to the velocity and the acceleration of the ball?

Sushant · Accepted Answer

Dear student,

Please find below the solution to the asked query:

Earth mass system:M is mass of earthR = radius of earthm = mass of any object  the gravitational force inside the earth at any distance x is F = GMmx R3so force is linearly decreases as body moves towards the center of earth so a =  GMmx R3m = GMx R3so a is directly proportional to xhence acceleration decreases continuously till the center of the earthwhile as a = vdvdxso vdvdx =  GMx R3or∫0v vdv = ∫Rx GMx dxR3so v22 = GMR3x22Rx = GMR3x22-R22or v =  GMR3x2-R2thus velocity increases as th body moves towards the center of earth 
It can also be observed if we know that the body is accelerating towards the center of earth although decreasing in magnitude

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If a hollow rod is passed through the centre of gravity of the earth and if a ball is passed into that hollow rod then what happens to the velocity and the acceleration of the ball?