Planet A has twice the mass of Planet B.From this information,what can we conclude about the free-fall acceleration at the surface of Planet A compared to that at the surface of Planet B?
A)The free-fall acceleration on Planet A must be twice as great as the free-fall acceleration on Planet B.
B)The free-fall acceleration on Planet A must be four times as great as the free-fall acceleration on Planet B.
C)The free-fall acceleration on Planet A is the same as the free-fall acceleration on Planet B.
D)The free-fall acceleration on Planet A is greater than the free-fall acceleration on Planet B, but we cannot say how much greater.
E)We cannot conclude anything about the free-fall acceleration on Planet A without knowing the radii of the two planets.

Question

Quizplus · Accepted Answer

The free-fall acceleration on a planet's surface depends on both its mass and radius (as per the formula $g = \frac{G \cdot M}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, and $r$ is the radius of the planet). Without knowing the radii of the planets, we cannot determine how the free-fall accelerations compare.

Planet a Has Twice the Mass of Planet B