Question

1. how would the density of a copper cylinder change if you had one that was double the mass of the original?

Explanation:

Step1: Recall density formula

Density $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume. For a solid like a copper - cylinder, if the mass doubles ($m_2 = 2m_1$), and assuming it is the same material and the expansion due to mass - increase is negligible (in normal conditions), the volume also doubles proportionally ($V_2=2V_1$) because of the uniform nature of the material.

Step2: Calculate new density

$
ho_1=\frac{m_1}{V_1}$, $
ho_2=\frac{m_2}{V_2}$. Substitute $m_2 = 2m_1$ and $V_2 = 2V_1$ into the density formula for the new situation: $
ho_2=\frac{2m_1}{2V_1}$.

Step3: Simplify the new - density expression

$
ho_2=\frac{2m_1}{2V_1}=\frac{m_1}{V_1}=
ho_1$.

Answer:

The density of the copper cylinder would not change.