physics question

Question

A planet of radius R and density ρ is struck by another planet with a much lower density. With time, the two coalesce into a new planet of radius 3R and a density of ½ ρ. By what factor is the surface gravity of the new planet stronger or weaker than that of the original planet?

Answer 1

Calculate the volume of the first planet V1 = 4/3 •π R³. The mass M1 of the first planet is V1• ρ.

Calculate the volume of the second planet V2 = 4/3•π (3R)³. The mass M2 is V2 • 1/2 ρ.

The force of attraction F1 on a mass m by the first planet is G 4/3 •π R³ρ • m/R².

The force of attraction F2 on a mass m by the second planet is G 4/3•π•27R³•1/2ρm/9R²

After cancelling like factors, F2/F1 = 3/2, the second (new) planet has 3/2 the gravitational strength of the first planet.

Please check my algebra.