A student sets up an experiment to investigate the pressure due to a liquid as shown - Scottish Highers Physics - Question 13 - 2018

Using the square-ruled paper provided, plot the values from the table given:

• Ensure that the x-axis (depth, $h$ in m) and y-axis (pressure, $p$ in kPa) are labeled correctly.
• Choose an appropriate scale for both axes (e.g., 1 cm = 10 m for depth and 1 cm = 1 kPa for pressure).
• Plot the points based on the data:
  • (10, 1.2)
  • (20, 2.5)
  • (40, 4.9)
  • (50, 6.2)
• Connect the points with a suitable line of best fit.

The gradient of the graph is calculated using:

$m = \frac{\Delta p}{\Delta h}$

Choose two points from your plotted graph:

1. For example, take point (10, 1.2 kPa) and (40, 4.9 kPa).

Now,

• Change in pressure, $\Delta p = 4.9 - 1.2 = 3.7$ kPa
• Change in depth, $\Delta h = 40 - 10 = 30$ m

Therefore, the gradient is:

$m = \frac{3.7}{30} \approx 0.123 \text{ kPa/m}$

To calculate the density of the liquid, use the relationship:

$p = \frac{\text{gradient} \times g}{1}$

Given the gradient calculated from the graph, substituting $g = 9.81 \text{ N/kg}$:

$\rho = \frac{0.123 \times 9.81}{1} \approx 1.21 \times 10^3 \text{ kg m}^{-3}$

Thus, the density of the liquid is approximately 1210 kg/m³.