Question

problem 16
if the earth somehow became 3 times more massive than it is now, but stayed the same size, our weight would increase by a factor of 9.
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false
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Explanation:

Step1: Recall gravitational - force formula

The gravitational force on the Earth's surface is given by $F = G\frac{Mm}{R^{2}}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of an object on the Earth's surface, and $R$ is the radius of the Earth. Our weight $W$ is equal to this gravitational force. If the mass of the Earth becomes $M'=3M$ and the radius remains the same ($R' = R$), then the new weight $W'=G\frac{M'm}{R'^{2}}=G\frac{3Mm}{R^{2}} = 3W$.

Answer:

FALSE