If you double the size (volume) of a substance but keep its mass per unit volume the same, how does its density change?

• A. The density remains the same.
• B. The density doubles.
• C. The density increases fourfold.
• D. The density is halved.

Answer: (A)

Verified step by step guidance

1. Recall the definition of density, which is mass per unit volume, expressed as \(\rho = \frac{m}{V}\), where \(\rho\) is density, \(m\) is mass, and \(V\) is volume.
2. Understand that if the mass per unit volume remains the same, it means the ratio \(\frac{m}{V}\) does not change even if the volume changes.
3. If the volume is doubled, write the new volume as \(V_{new} = 2V\), and since the mass per unit volume is constant, the new mass must be \(m_{new} = 2m\) to keep the ratio the same.
4. Calculate the new density using the new mass and new volume: \(\rho_{new} = \frac{m_{new}}{V_{new}} = \frac{2m}{2V}\).
5. Simplify the expression to see that \(\rho_{new} = \frac{2m}{2V} = \frac{m}{V} = \rho\), which shows the density remains the same.