problem 16\nif the earth somehow became 3 times more massive than it is now, but stayed the same size, our…

problem 16\nif 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.\ntrue\nfalse\nsubmit\nhint\nfeedback\ni give up!\n1 submission(s) remaining\nhints: 0 for a 0% deduction. hints remaining: 0\nfeedback: 1% deduction per feedback.

problem 16\nif 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.\ntrue\nfalse\nsubmit\nhint\nfeedback\ni give up!\n1 submission(s) remaining\nhints: 0 for a 0% deduction. hints remaining: 0\nfeedback: 1% deduction per feedback.

Answer

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