Planet A has twice the mass of planet B.Experiments determine that a bowling ball on planet A weighs eight times as much as it does on planet B.Relative to the radius of planet B,what is the radius of planet A?
A) Planet A has four times the radius of planet B.
B) Planet A has twice the radius of planet B.
C) Planet A has the same radius as planet B.
D) Planet A has half the radius of planet B.

Question

Quizplus · Accepted Answer

The weight of an object on a planet is directly proportional to the mass of the planet and inversely proportional to the square of the radius of the planet. Given that the bowling ball weighs eight times as much on planet A as on planet B and planet A has twice the mass of planet B, we can use the formula for gravitational force (F = Gm1m2/r^2, where G is the gravitational constant, m1 and m2 are the masses involved, and r is the distance between the centers of the two masses) to determine the relationship between the radii of the two planets. The increase in weight by a factor of 8 due to doubling the mass implies that the radius must be halved to maintain the relationship, as the weight (or gravitational force) varies inversely with the square of the radius.

Planet a Has Twice the Mass of Planet B