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 :
11.2
15.8
5.6
7.9
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2024
The escape speed (v_e) from a spherical body of mass M and radius R is given by v_e = sqrt(2GM/R). The mass M can be expressed in terms of density (rho) and volume (V = 4/3 * pi * R^3) as M = rho * (4/3 * pi * R^3). Substituting this into the escape speed formula: v_e = sqrt(2G * (rho * 4/3 * pi * R^3) / R) = sqrt(8/3 * pi * G * rho * R²) = R * sqrt(8/3 * pi * G * rho). This shows that v_e is proportional to R * sqrt(rho).