Suggest which of p, or p. is likely to be the more accurate value for the density of the modelling clay. Justify your answer by referring to the procedure.

Here are the solutions to the questions:

Question (c):

• iii) Record the new reading $V_f$ of the measuring cylinder in Fig. 2.5 with the rectangular block of modelling clay in the water.

  • Step 1: Read the final volume from the measuring cylinder scale. The scale has major markings every $25 \text{ cm}^3$ and minor markings every $5 \text{ cm}^3$. The water level is at the second mark above $150 \text{ cm}^3$. $$V_f = 150 \text{ cm}^3 + (2 \times 5 \text{ cm}^3)$$ $$V_f = 150 \text{ cm}^3 + 10 \text{ cm}^3$$ $$V_f = \boxed{\text{160 cm}^3}$$

• iv) Use your results from (c)(i) and (c)(iii) to calculate $\rho_2$.

  • Step 1: Recall the necessary values. From (a)(iii), the weight $w = 1.2 \text{ N}$. The constant $k = 100 \text{ g/N}$. From (c)(i), the initial volume of water $V_2 = 155 \text{ cm}^3$. From (c)(iii), the final volume of water $V_f = 160 \text{ cm}^3$.
  • Step 2: Calculate the volume of the clay block. The volume of the clay block is the difference between the final and initial water volumes: $$V_{\text{clay}} = V_f - V_2 = 160 \text{ cm}^3 - 155 \text{ cm}^3 = 5 \text{ cm}^3$$
  • Step 3: Substitute the values into the given equation for density $\rho_2$. $$\rho_2 = \frac{w \times k}{(V_f - V_2)}$$ $$\rho_2 = \frac{1.2 \text{ N} \times 100 \text{ g/N}}{5 \text{ cm}^3}$$
  • Step 4: Perform the calculation. $$\rho_2 = \frac{120 \text{ g}}{5 \text{ cm}^3}$$ $$\rho_2 = \boxed{\text{24 g/cm}^3}$$

• v) Suggest which of $\rho_1$ or $\rho_2$ is likely to be the more accurate value for the density of the modelling clay. Justify your answer by referring to the procedure.

  • Suggestion: $\rho_2$ is likely to be the more accurate value.
  • Justification: The value $\rho_1$ was calculated using direct measurements of the block's dimensions ($l, b, h$). Modelling clay may not be a perfectly regular rectangular block, making accurate measurement of its dimensions difficult and prone to error. The value $\rho_2$ was calculated using the displacement method, which measures the actual volume of the object by the amount of water it displaces, regardless of its exact shape. This method is generally more reliable for objects that may not have perfectly regular geometric shapes.