Physics 5054/11 — October/November 2015

Walkthrough

The question asks to identify what the readings from a measuring cylinder experiment tell us about a stone. The image shows two states: water alone, and water with a submerged stone.

1. Initial Reading ($V_1$): The left cylinder contains only water. The reading on the scale gives the volume of the water.
2. Final Reading ($V_2$): The right cylinder contains the water and the submerged stone. The water level has risen because the stone takes up space. The new reading represents the total volume of (water + stone).
3. Calculating Volume: By Archimedes' principle of displacement, the volume of the submerged object is equal to the volume of fluid it displaces. Mathematically, $V_{\text{stone}} = V_{\text{final}} - V_{\text{initial}}$. Thus, the difference between the two readings is the volume of the stone.
4. Calculating Density: Density ($\rho$) requires two pieces of information: mass ($m$) and volume ($V$), using the formula $\rho = \frac{m}{V}$. The measuring cylinder only provides volume information. Without the mass of the stone (which would be measured on a balance before lowering it in), the density cannot be determined from these readings alone. Therefore, the difference is a volume, not a density.

Key Takeaways

• The displacement method (using a measuring cylinder and water) is used to find the volume of an irregular solid that does not dissolve in water.
• The volume of the object is the difference between the final water level (with object) and the initial water level (without object).
• Density is a derived quantity ($\rho = m/V$) and requires both mass and volume measurements; a volume measurement alone is insufficient to state the density.

Common Mistakes

• Confusing volume and density: Students may think the reading directly gives density because the experiment is "to find the density". However, the cylinder only measures volume; mass is the missing variable.
• Misinterpreting the final reading: The final reading ($V_2$) is the total volume of water and stone combined, not the volume of the stone alone. Option D is incorrect for this reason.
• Ignoring the initial reading: Option A suggests the difference is density. This is a common error where students forget that density is a ratio of mass to volume, not just a volume difference.

Things to Be Careful About

• Full submersion: For the displacement method to work correctly, the stone must be fully submerged and not touch the sides/bottom in a way that traps air, though the diagram implies a standard setup.
• Meniscus reading: In a real experiment, readings should be taken at the bottom of the meniscus at eye level to ensure accuracy, though this is a conceptual question.
• Units: Volume is typically in $\text{cm}^3$ or $\text{ml}$ ($1 \text{ cm}^3 = 1 \text{ ml}$). Density would be in $\text{g/cm}^3$ or $\text{kg/m}^3$.