A stone hangs from a spring balance. In air the balance reads 24 N; fully under water it reads 18 N…

Step 1. (a) $24\ \text{N} - 18\ \text{N} = 6\ \text{N}$.

Step 2. (b) $V = \dfrac{6\ \text{N}}{1000\ \text{kg/m}^3 \times 9.8\ \text{m/s}^2} = 6.12 \times 10^{-4}\ \text{m}^3$.

Step 3. (c) Mass $\dfrac{24\ \text{N}}{9.8\ \text{m/s}^2} = 2.45\ \text{kg}$, so density $\dfrac{2.45\ \text{kg}}{6.12 \times 10^{-4}\ \text{m}^3} = 4000\ \text{kg/m}^3$.

Step 4. (d) $\dfrac{4000\ \text{kg/m}^3}{1000\ \text{kg/m}^3} = 4$, a pure number.