The free-fall acceleration on Planet A is one-sixth what it is on Planet B,and the radius of the Planet A is one-fourth that of Planet B.The mass of Planet A is what fraction of the mass of Planet B?
A)1/6
B)1/16
C)1/24
D)1/96
E)1/12

Question

Quizplus · Accepted Answer

The gravitational force equation is F = G(m1*m2)/r^2. The acceleration due to gravity is g = G*M/r^2. Given g_A = (1/6)g_B and r_A = (1/4)r_B, we have (G*M_A)/(r_A^2) = (1/6)(G*M_B)/(r_B^2). Substituting r_A = (1/4)r_B, we get M_A/M_B = (1/6)*(1/16) = 1/96.

The Free-Fall Acceleration on Planet a Is One-Sixth What It