If two planets,A and B,have the same value of g on their surfaces,which of the following scenarios cannot be true? (M_A and M_B are their masses and R_A and R_B are their radii.)

Question

Quizplus · Accepted Answer

The acceleration due to gravity on the surface of a planet is given by g = GM/R^2, where M is the mass of the planet, R is the radius of the planet, and G is the gravitational constant. Since the value of g is the same for planets A and B, we can write:

GM_A/R_A^2 = GM_B/R_B^2

Dividing the two equations, we get:

(M_A/M_B) = (R_A/R_B)^3

For scenario E, we have:

M_A = 4M_B and R_A = 3R_B

Substituting these values, we get:

(4M_B/M_B) = (3R_B/R_B)^3

4 = 27

This is clearly not true, so scenario E cannot be true.

If Two Planets,A and B,have the Same Value of G