Prove that the value of 'g' decreases as if a body is taken downward from the Earth.
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We all know that gravity decreases as the distance between the two increases. Hence
F=GMmr2.F=GMmr2.Hence acceleration
g=Fm=GMr2g=Fm=GMr2due to gravity is inversely proportional to the distance between the two bodies.Then why does the gravity decrease as we go deep into the earth?
annajj:
The pull of gravity is zero at the center, since the entire planet pulls on you from all directions. It falls off from 1g to 0g (more or less smoothly, but not uniformly) as you go from the surface to the center. But due to the greater density of the core, it actually increases until you reach the bottom of the mantle.
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If the depth increases the mass of the earth decreses. If we consider the density of earth to be uniform the mass of the earth at some radius 'R' should be equal to 4/3πR^3 into the density. If we substitute this mass in the formula which give acceleration due to gravity which is GM/R^2 the factor of R^2 gets cancelled. Giving us acceleration due to gravity equal to 4/3πR*(density). At the surface of the earth this value will be maximum because R will be max. When R becomes less ( i.e when depth increases) this value also decreases. Hence, acceleration due to gravity decreases with increase in depth. I hope this answers your question.
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