Escape velocity
- The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is : Answer: 4. 4v Key idea: v_e=√(2GM/R) and M=4/3π R³ρ , so v_e∝ Rsqrtρ . Same density and radius four times as large gives v_e'=4v . Option 4. 1
- The ratio of escape velocity at earth (v_e) to the escape velocity at a planet (v_p) whose radius and mean density are twice as that of earth is : Answer: 2. 1 : 2√(2) Key idea: v_e=√(2GM/R)=R√(8π Gρ/3) , so v_e∝ Rsqrtρ . Planet: radius 2R , density 2ρ , so v_p=v_e×2×sqrt2=2sqrt2 v_e .... 1