Question

By what factor would your weight change if Earth's diameter were tripled and its mass were quintupled?

Answer 1

We have that our weight on Earth equal to:

$$W = \frac {4 \cdot G \cdot m \cdot M}{d ^ {2}}$$

where:

$G$ is a gravitational constant;

$M$ is a mass of Earth;

$m$ is your mass;

$d$ is a diameter of Earth.

So, when the Earth's mass were quintupled and Earth's diameter were tripled we will have:

$$W = \frac {4 \cdot G \cdot m \cdot 5 \cdot M}{\left(3 \cdot d\right) ^ {2}} = \frac {5}{9} \cdot \frac {4 \cdot G \cdot m \cdot M}{d ^ {2}}.$$

So the factor by which our weight would changed if the Earth's mass were quintupled and Earth's diameter were tripled is $\frac{5}{9}$ .

Answer: $\frac{5}{9}$ .