Suppose you are suddenly transported to a planet with one-fourth the radius of Earth but the same mass as Earth.Your weight would ________ by a factor of ________.
A) increase; 4
B) increase; 16
C) decrease; 4
D) decrease; 16

Question

Quizplus · Accepted Answer

Your weight would increase because the gravitational force depends inversely on the square of the distance from the center of mass. Since the radius is one-fourth that of Earth, but the mass remains the same, the gravitational force (and thus your weight) would increase by a factor of (1/(1/4)^2) = 16.

Suppose You Are Suddenly Transported to a Planet with One-Fourth