A planet of radius R has density ρ(r)=ρ₀(1−r/R). The ratio g(R/2)/g(R) is:

Question

G1 Physics · Accepted Answer

M(r)=4πρ₀∫₀ʳ(r'²−r'³/R)dr'. At r=R/2, M=4πρ₀R³(5/192); at R, M=4πρ₀R³(1/12). Since g=GM/r², g(R/2)/g(R)=4[M(R/2)/M(R)]=4×(5/16)=5/4.