Density: Question 3

Worked solution

Part (a): Describing the displacement method

1. Place the dry stone on a balance and record its mass, $m$.
2. Partly fill a measuring cylinder with water and record the initial volume reading, $V_1$.
3. Tie the stone to a thin thread and lower it gently into the cylinder until it is fully submerged, then record the new volume reading, $V_2$.

The stone’s volume equals the rise in the water level, $V = V_2 - V_1$, because the stone pushes aside (displaces) its own volume of water.

Part (b): Calculating the density

Find the volume from the two readings:

$V = V_2 - V_1 = 57.5 - 42.0$

$V = 15.5\text{ cm}^3$

Divide the mass by this volume:

$\rho = \frac{m}{V} = \frac{38.7\text{ g}}{15.5\text{ cm}^3}$

$\rho = 2.4967\ldots\text{ g/cm}^3$

Round to 3 significant figures:

$\rho \approx \boxed{2.50\text{ g/cm}^3}$

Part (c): A precaution for accuracy

The student should view the water surface at eye level and read from the bottom of the meniscus, to avoid a parallax error when recording $V_1$ and $V_2$. (Alternatively: lower the stone in slowly to prevent splashing water out of the cylinder, or check that no air bubbles cling to the stone’s surface, since trapped air would make the measured volume too large.)

Final answers

• (a) Weigh the stone, record the water level, submerge the stone, record the new water level; volume = rise in level.
• (b) Density $=$ $2.50\text{ g/cm}^3$ (3 s.f.)
• (c) Read the meniscus at eye level (or an equivalent valid precaution).