Plot a graph of M on the vertical axis and T 2 on the horizontal axis, starting both axes from the origin (0,0). Determine the slope S of the graph.

I need the actual experimental readings to complete questions ix, x, and xi. The image provided only shows the instructions and blank spaces for your answers.

However, I can explain how to approach each part once you have your data.

ix. Tabulate your readings in the space provided below:

You should create a table with columns for your measured values. Based on the subsequent questions, you will likely have readings for 'M' (mass or similar quantity) and 'T' (period or time). You will also need to calculate 'T²'.

Here's an example of how you might structure your table:

S/N	M (units)	T (units)	T² (units²)
1
2
3
4
5
6

• S/N: Serial Number for each reading.
• M: Your measured values for M, with appropriate units (e.g., kg, g).
• T: Your measured values for T, with appropriate units (e.g., s).
• T²: The square of your T values, with appropriate units (e.g., s²).

x. Plot a graph of M on the vertical axis and T² on the horizontal axis, starting both axes from the origin (0,0).

To plot the graph:

• Draw two perpendicular axes on graph paper.
• Label the vertical axis 'M' and include its units.
• Label the horizontal axis 'T²' and include its units.
• Ensure both axes start from the origin (0,0).
• Choose appropriate scales for both axes so that your data points spread across most of the graph paper.
• Plot each data point (T², M) from your table.
• Draw the best-fit straight line through your plotted points.

xi. Determine the slope S of the graph.

To determine the slope (S) of the graph:

• Choose two distinct points on your best-fit line (not necessarily actual data points). Let these points be $(T_1^2, M_1)$ and $(T_2^2, M_2)$.
• The slope S is calculated using the formula: $$S = \frac{\text{Change in M}}{\text{Change in T}^2} = \frac{M_2 - M_1}{T_2^2 - T_1^2}$$
• Substitute the coordinates of your chosen points into the formula and calculate the value of S.
• Include the correct units for the slope (units of M / units of T²).

Once you have your readings, send them over, and I can help you with the calculations and plotting!