Suppose there are two planets, 1 and 2, having the same density but their radii are R1 and R2 respectively, where R1 > R 2. The accelerations due to gravity on the surface of these planets are related as

The acceleration due to gravity (g) on a planet's surface is defined by the formula g = GM/R², where G is the gravitational constant, M is the mass, and R is the radius. Since mass (M) is the product of density (ρ) and volume (V), and assuming the planet is a sphere, M = ρ × (4/3)πR³. Substituting this into the gravity formula yields g = G(ρ × 4/3πR³)/R², which simplifies to g = (4/3)πGρR. This demonstrates that for planets with the same density, the acceleration due to gravity is directly proportional to the radius (g ∝ R). Given that planet 1 and planet 2 have the same density and R1 > R2, it follows that g1 must be greater than g2.