Question

(b) lequel est plus lourd: 50 cm³ dor ou 50 cm³ daluminium? expliquer

Explanation:

Step1: Recall the formula for mass

The formula that relates mass (\(m\)), volume (\(V\)) and density (\(
ho\)) is \(m =
ho\times V\).

Step2: Analyze the given volumes

We are given that the volume of gold (\(V_{gold}\)) and the volume of aluminium (\(V_{aluminium}\)) are both \(50\space cm^3\), so \(V_{gold}=V_{aluminium} = 50\space cm^3\).

Step3: Recall the densities of gold and aluminium

The density of gold (\(
ho_{gold}\)) is approximately \(19.3\space g/cm^3\) and the density of aluminium (\(
ho_{aluminium}\)) is approximately \(2.7\space g/cm^3\). Since \(
ho_{gold}>
ho_{aluminium}\) and \(V_{gold} = V_{aluminium}\), using the formula \(m=
ho\times V\), when the volume is the same, the substance with the higher density will have a higher mass.

Step4: Calculate the masses (optional for comparison)

For gold: \(m_{gold}=
ho_{gold}\times V_{gold}=19.3\space g/cm^3\times50\space cm^3 = 965\space g\)
For aluminium: \(m_{aluminium}=
ho_{aluminium}\times V_{aluminium}=2.7\space g/cm^3\times50\space cm^3=135\space g\)
Since \(965\space g> 135\space g\), \(50\space cm^3\) of gold is heavier.

Answer:

\(50\space cm^3\) of gold is heavier.