The mass and radius of four hypothetical planets A, B, C and D are given below in terms of the mass ( M ) and radius ( R ) of the Earth: Planet A: Mass M , Radius R Planet B: Mass 2M , Radius R/2 Planet C: Mass 4M , Radius 2R Planet D: Mass 8M , Radius 4R Which of these planets has the highest escape velocity for an object on its surface?

Step-by-step solution

The escape velocity of a planet is given by v_e = 2GM R , which means v_e M R . Calculating the ratio M R for each planet: For Planet A: M R = 1 For Planet B: 2M R/2 = 4 For Planet C: 4M 2R = 2 For Planet D: 8M 4R = 2 Since Planet B has the highest value of the ratio M R , it yields the highest value for M R and thus the highest escape velocity. Answer: Planet B