Answer
We can rank the planets according to the mass per unit volume:
$1 \gt 2 \gt 3 \gt 4$
Work Step by Step
In part (a), we ranked the planets according to mass as follows:
$1 = 2 \gt 3 = 4$
Since $R_1 \lt R_2$, planet 1 is smaller in volume than planet 2 but they have the same mass. Therefore, the mass per unit volume of planet 1 is greater than that of planet 2.
Since $R_3 \lt R_4$, planet 3 is smaller in volume than planet 4 but they have the same mass. Therefore, the mass per unit volume of planet 3 is greater than that of planet 4.
Since $R_2 = R_3$, planet 2 and planet 3 have the same volume, but planet 2 has a greater mass than planet 3. Therefore, the mass per unit volume of planet 2 is greater than that of planet 3.
We can rank the planets according to the mass per unit volume:
$1 \gt 2 \gt 3 \gt 4$
