A solid sphere P and two hollow spherical shells Q and S are concentric. Their radii are R, 2R and 3R and their densities are ρ₁, ρ₂ and ρ₃. Given ρ₂ = (ρ₁ + ρ₃)/2. If the gravitational fields at points A and B shown are equal, find 10ρ₃/ρ₁.

Question

G1 Physics · Accepted Answer

Step 1: Apply the shell theorem. Inside a uniform spherical shell the field is zero; inside a uniform solid sphere only the enclosed mass contributes. Step 2: Superpose the fields of the solid sphere and shells/cavity with correct signs. Step 3: Equate the fields at the stated points or evaluate the requested ratio. Final: 2.