Question

The gravitational acceleration on the surface

of planet Zeb is the same as on the surface of
the earth, but planet Zeb has twice the radius
of the earth. What must be the ratio of the mass of
planet Zeb to the mass of earth?
1) 1/8
2)2
3)8
4) 1/4
5) 1 (the same since g is the same)
6) 1/10
7)4
8)10
9)6

Answer 1

The ratio of the mass of planet Zeb to the mass of Earth must be 8.

Step-by-step explanation:

The gravitational acceleration on the surface of a planet is determined by the mass of the planet and its radius. The equation is g = GM/r^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.

If we assume that the gravitational acceleration on the surface of both planets is the same, we can set the equation for Earth equal to the equation for planet Zeb and solve for the ratio of the mass of planet Zeb to the mass of Earth.

g(earth) = GM(earth)/r(earth)^2 = GM(zeb)/r(zeb)^2

We know that r(zeb) = 2 * r(earth)

so,

GM(earth)/r(earth)^2 = GM(zeb)/(2*r(earth))^2

GM(zeb)/GM(earth) = (2*r(earth))^2 /r(earth)^2

GM(zeb)/GM(earth) = 4*4

GM(zeb)/GM(earth) = 16

So the ratio of the mass of planet Zeb to the mass of Earth is 16/1 = 8