Question

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

Answer 1

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

Answer 2

Answer:

(C)=>Center of the earth

Explanation:

As Earth is flattened at the pole , radius of the equator is greater than radius of the pole. Since gravity is inversely proportional to the radius. This factor reduces the net gravity at equator compared to the pole.

Hence, acceleration is zero at centre of earth