Variation Of Acceleration Due To Gravity With Depth

Variation Of Acceleration Due To Gravity With Depth — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.

Variation of Acceleration due to Gravity with Depth Valid for depths d less than or equal to the radius R. Assumes the planet is a solid sphere with uniform mass density. Assume Earth is a homogeneous sphere of radius R and mass M. Gravity at surface: g = GM/R 2. At depth d, distance from center is r = R - d. Only the mass enclosed within radius r (M') contributes to gravity. M' is proportional to volume: M' = M (r/R) 3. Gravity at depth: g d = GM'/r 2. Substitute M' and simplify: g d = GM(r)/R 3 = (GM/R 2) (r/R). Substitute r = R - d: g d = g (1 - d/R). d <= R Uniform density assumption required Thinking gravity increases with depth because you are closer to the core (true for non-uniform density, false for uniform sphere models). Using the inverse square law (1/r 2) inside the shell (incorrect; field is linear inside a uniform sphere).