when the height of the cylinder increased by a factor of 5, from 100 m to 500 m, what happened to the…

Explanation:

Step1: Recall gravitational - potential - energy formula

The gravitational potential energy formula is $U = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height.

Step2: Analyze the change in height

Let the initial height be $h_1 = 100m$ and the final height be $h_2 = 500m$. The ratio of the final height to the initial height is $\frac{h_2}{h_1}=\frac{500}{100}=5$. Since $U = mgh$ and $m$ and $g$ are constant, the ratio of the final potential energy $U_2$ to the initial potential energy $U_1$ is $\frac{U_2}{U_1}=\frac{mgh_2}{mgh_1}=\frac{h_2}{h_1}$.

Answer:

It increased by a factor of 5.