gravitation inside earth

Question

Gravitational force on a mass inside Earth (uniform density) at distance r < R from center varies as:

RankGuru · Accepted Answer

Using Gauss's Law for gravity or Shell Theorem:
- Only the mass *inside* the sphere of radius $r$ exerts a net force.
- $M_{enc} = ho 	imes \frac{4}{3}\pi r^3$. Since density $ho$ is uniform, $M_{enc} \propto r^3$.
- Force $F = \frac{G M_{enc} m}{r^2} \propto \frac{r^3}{r^2} = r$.
- Thus, the field increases linearly from zero at the center to $g$ at the surface.

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gravitation inside earth

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