Question

Two planets, alice and bob, have the same radius. Alice has a greater density than bob. Which has the higher escape velocity?

Answer 1

Answer:

Since Alice has a greater density it will also have a greater mass

Density = mass / volume

The potential energy at the surface of Alice will be greater and a higher kinetic energy will be required to escape  the planet's gravitational pull.

PE = K M / R      potential at surface is greater because mass is greater

KE = 1/2 M v^2     greater velocity required to overcome PE