How does the force of gravity F vary inside t | vedclass

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(A) The gravitational force $F$ on a mass $m$ at a distance $r$ from the center of the Earth (where $r < R_e$) is given by $F = \frac{G M_r m}{r^2}$.A

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$F \propto r$

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(A) The gravitational force $F$ on a mass $m$ at a distance $r$ from the center of the Earth (where $r Assuming the Earth has a uniform density $\rho$,the mass $M_r$ contained within a sphere of radius $r$ is $M_r = \rho \cdot \frac{4}{3} \pi r^3$.Substituting $M_r$ into the force equation: $F = \frac{G m}{r^2} \cdot \rho \cdot \frac{4}{3} \pi r^3$.Simplifying this,we get $F = (\frac{4}{3} \pi G \rho m) r$.Since $G, \pi, \rho, m$ are constants,it follows that $F \propto r$.

How does the force of gravity $F$ vary inside the Earth at a distance $r$ from the center,where $r < R_e$?

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