Question

3.3.2 test (cst): forces
question 1 of 20
planets a and b have the same mass, but planet a is half the size of planet b. which statement correctly explains the weight you would experience on each planet?
a. you would weigh more on planet a because the distance between you and the planets center of gravity would be smaller.
b. you would weigh less on planet a because the distance between you and the planets center of gravity would be smaller.
c. you would weigh the same on both planets because the masses of the planets are the same.
d. you would weigh the same on both planets because your mass would be the same on both.

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force \(F = G\frac{Mm}{r^{2}}\), where \(G\) is the gravitational constant, \(M\) is the mass of the planet, \(m\) is your mass, and \(r\) is the distance from the center of the planet to you (which is related to the size of the planet).

Step2: Analyze the effect of planet size on gravitational force

Planets \(A\) and \(B\) have the same mass (\(M\)) and your mass (\(m\)) is the same. Since planet \(A\) is half the size of planet \(B\), the distance \(r\) from you to the center of planet \(A\) is smaller than that of planet \(B\).
As \(F\propto\frac{1}{r^{2}}\) (when \(M\) and \(m\) are constant), a smaller \(r\) means a larger \(F\). Weight is the gravitational force acting on you.

Answer:

A. You would weigh more on planet A because the distance between you and the planet's center of gravity would be smaller.