Question

by what factor would a persons weight at the surface of earth change if earth had its present size but only one - third its present mass?
a person would weight the same
a person would weight three times as much
a person would weight only one - ninth as much
a person would weight only one - third as much
a person would weight nine times as much
question 10
if the distance between two objects is doubled, what happens to the gravitational force between them?
the gravitational force becomes one - half as strong
the gravitational force becomes twice as strong
the gravitational force is not affected
the gravitational force becomes one - fourth as strong
the gravitational force becomes four times as strong

Explanation:

Step1: Recall gravitational - force formula

The gravitational force formula is $F = G\frac{Mm}{r^{2}}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $M$ is the mass of the larger object (e.g., Earth), $m$ is the mass of the smaller object (e.g., a person), and $r$ is the distance between the centers of the two objects.

Step2: Analyze the first - question

If the radius of the Earth $r$ remains the same and the mass of the Earth $M$ becomes $\frac{1}{3}M$, then the new gravitational force $F'$ is $F'=G\frac{\frac{1}{3}Mm}{r^{2}}=\frac{1}{3}G\frac{Mm}{r^{2}}=\frac{1}{3}F$. So a person would weigh only one - third as much.

Step3: Analyze the second - question

If the distance between two objects is doubled, i.e., $r$ becomes $2r$, then the new gravitational force $F''$ is $F'' = G\frac{Mm}{(2r)^{2}}=G\frac{Mm}{4r^{2}}=\frac{1}{4}F$. So the gravitational force becomes one - fourth as strong.

Answer:

A person would weight only one - third as much
The gravitational force becomes one - fourth as strong