Planet A has nine times the mass of planet B,but they have equal radii.How fast would you have to launch a rocket from planet A for it to escape the pull of its gravity,if the corresponding speed for planet A is 10 m/s?
A) 3 m/s
B) 10 m/s
C) 30 m/s
D) 90 m/s

Question

Quizplus · Accepted Answer

Escape velocity is given by the formula: Ve= sqrt(2GM/R), where Ve is the escape velocity, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet. 
Since the radius is the same for both planets, we can use the ratio of their masses (9:1) to find the ratio of their escape velocities. 
Ve(A)/Ve(B) = sqrt(2GM(A)/R)/sqrt(2GM(B)/R) 
Ve(A)/Ve(B) = sqrt(M(A)/M(B)) 
Ve(A)/10 = sqrt(9) 
Ve(A) = 30 m/s

Planet a Has Nine Times the Mass of Planet B,but