Question

The escape speed from Planet X is 20000 m/s . Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?

Answer 1

Escape speed
V₀ = √(2GM/r)
where M is mass of the central body and r is radius of the central body.

First we have to convert "twice as dense" to mass.
Call planet X mass m.
planet Y mass m₂ = density x volume. since radius is the same, volume is the same. So if the density is twice, than the mass is twice.

back to V₀ = √(2GM/r)
If you double the mass, keeping everything else constant, then V₀ goes up by √2 = 1.414

20000 m/s x √2 = 28284.27 m/s