Potential Inside Uniform Sphere — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Potential Inside Uniform Sphere This formula describes the gravitational potential at a distance 'r' from the center of a sphere, provided the sphere has a uniform mass density and the point 'r' is located inside the sphere (r R). Determine the mass enclosed within radius r, M(r), assuming uniform density ( = M/ (4 R 3 )). Apply Newton's Shell Theorem, treating the enclosed mass M(r) as a point mass. Use the differential form of potential: dV = - G M(r) r 2 dr. Integrate the potential from r=0 to the final position r, resulting in the given quadratic form. r R r 0 Confusing the potential inside the sphere with the potential at the surface (V(R) = -GM/R). Assuming the potential is linear with distance r. Using the formula for the potential of a point mass instead of accounting for the enclosed mass M(r).