A student carries out an investigation to determine the gravitational field strength on Earth, using a simple pendulum - Scottish Highers Physics - Question 14 - 2022

To calculate the gradient, choose two points on the line of best fit. For example, let’s select the points:

• Point 1: (0.20, 0.85)
• Point 2: (1.10, 4.55)

The formula for the gradient (m) is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates of the points:

$m = \frac{4.55 - 0.85}{1.10 - 0.20} = \frac{3.70}{0.90} = 4.112\, (s^2\, m^{-1})$

Thus, the gradient of the graph is approximately 4.1 (s²/m).

The gravitational field strength g can be determined using the rearranged formula:

$g = \frac{4\pi^2}{\text{gradient}}$

Assuming the gradient calculated above is approximately 4.1, we have:

$g = \frac{4\pi^2}{4.1}$

Using the value of π as approximately 3.14, we find:

$g = \frac{4 \times (3.14)^2}{4.1} \approx \frac{39.4784}{4.1} \approx 9.62\, N\, kg^{-1}$

Thus, the determined gravitational field strength g is approximately 9.62 N kg⁻¹.