Two planets have the same surface gravity,but planet B has twice the radius of planet A.If planet A has mass m,what is the mass of planet B?
A)m/
B)m
C)m
D)4m
E)m/4

Question

Two planets have the same surface gravity,but planet B has twice the radius of planet A.If planet A has mass m,what is the mass of planet B?
A)m/ 
B)m 
C)m 
D)4m 
E)m/4

Quizplus · Accepted Answer

The surface gravity of the two planets is the same, which means that their gravitational force on an object of mass m is equal. Therefore, using the formula for surface gravity g = GM/R^2 (where G is the gravitational constant), we can write:

g_A = GM/R_A^2
g_B = GM/R_B^2

Since g_A = g_B, we can set the two equations equal to each other and solve for M_B/M_A:

g_A = g_B
GM_A/R_A^2 = GM_B/R_B^2
M_B/M_A = R_B^2/R_A^2 = (2R_A)^2/R_A^2 = 4

Therefore, the mass of planet B is 4 times the mass of planet A, or 4m.

Two Planets Have the Same Surface Gravity,but Planet B Has