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Variation in acceleration due to gravity (g) with depth

As we go deeper from the earth suface the gravity starts decreasing but formulla is ‘F=G*m*M/r2 where distance between the object and the earth is r2 which is inversally proportional to the ‘g’ then why as we go deeper from the earth suface the gravity starts decreasing; it should be increased because distance between the earth and the object is less. but it start decreasing why?

Prince Kumar Asked

Answer:

When we go deeper into earth, the attraction at that point is due to a sphere of earth of radius (R – d) where d is the depth below the surface of earth.

 

Let a body of mass m be kept on the surface of earth. The force exerted by earth on it,

F_{surface}=mg=\frac{GMm}{R^{2}} where M is the total mass of earth and R is the radius of earth.

But, M = \frac{4\pi R^{3}\rho }{3}

Substituting for M,

mg = \frac{4\pi G\rho m R}{3}

or  (more…)

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