Escape speed from the Earth is close to 11.2 km s⁻¹. On another planet whose radius is half of the Earth's radius and whose mass density is four times that of the Earth, the escape speed in km s⁻¹ will be close to:

Escape speed is given by v_esc = √(2GM/R). For a uniform sphere, M = (4/3)πR³ρ, so v_esc = √[(8πGρ/3)] × R, i.e. v_esc ∝ R√ρ. For the new planet, R' = R/2 and ρ' = 4ρ, so R'√ρ' = (R/2) × √(4ρ) = (R/2) × 2√ρ = R√ρ. Thus the escape speed remains the same as Earth's, approximately 11.2 km s⁻¹.