Suppose you are suddenly transported to a planet with 1/4 the mass of Earth but the same radius as the Earth. Your weight would _________ by a factor of _________.
A) increase; 4
B) increase; 16
C) decrease; 4
D) decrease; 16
E) increase; 2

Question

Quizplus · Accepted Answer

Weight is directly proportional to mass, so if the planet has 1/4 the mass of Earth, then your weight would decrease by a factor of 4 (choice C). This can be calculated using the formula W = mg, where W is weight, m is mass, and g is gravitational acceleration. On the new planet, the value of g would be 1/4 of its value on Earth, since 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. Therefore, your weight would be 1/4 of what it is on Earth, or a decrease by a factor of 4.

Suppose You Are Suddenly Transported to a Planet with 1/4