# NTSE physics question The acceleration due to gravity is zero at (a) Poles (b) equator (c) center of earth (d) None of these Please explain! Thanks

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2015-10-10T01:32:27+05:30

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Acceleration due to gravity is 0 at the center of Earth.

g' = g r / R

mass of Earth = M = 4π/3  R³ * d , where R = radius and d = density
g = G M / R²  using Newtons gravity equation.
= G 4π/3 R³ * d /R² =  G 4π/3 d R

At a radius r < R, the mass that contributes to gravity is only that contained inside the sphere of radius r.  The spherical shell between radii  r to R, does not contribute.  This is because the attraction forces from all directions will cancel one another.

g' = G M' / r²  = G (4π/3 r³ d) / r² = G 4π/3 * r d

g'/g =  r/R

so  when r = 0,  g' = 0