Use Table 1.2 to plot a graph of T on the y-axis and m on the x-axis. Draw a straight line of best fit. A student suggests that the mass m of the bob is directly proportional to the period T. State whether the readings support this suggestion. Justify your answer by reference to the graph line.

Here are the solutions to the questions:

Question 1 (d):

• i) Use Table 1.2 to plot a graph of T on the y-axis and m on the x-axis. Draw a straight line of best fit.

  • Step 1: Plot the data points from Table 1.2 on the graph grid.
    • For $m = 100 \text{ g}$, $T = 1.375 \text{ s}$
    • For $m = 150 \text{ g}$, $T = 1.380 \text{ s}$
    • For $m = 200 \text{ g}$, $T = 1.380 \text{ s}$
    • For $m = 250 \text{ g}$, $T = 1.390 \text{ s}$
    • For $m = 300 \text{ g}$, $T = 1.370 \text{ s}$
    • For $m = 350 \text{ g}$, $T = 1.385 \text{ s}$ Plot each $(m, T)$ pair as a distinct point on the graph.
  • Step 2: Draw a straight line of best fit. Observe the plotted points. They are clustered very closely around $T \approx 1.38 \text{ s}$. Draw a straight line that best represents the general trend of these points. This line will be approximately horizontal, indicating that the period $T$ is largely independent of the mass $m$.

• ii) A student suggests that the mass $m$ of the bob is directly proportional to the period $T$. State whether the readings support this suggestion. Justify your answer by reference to the graph line.

  • Statement: The readings do not support the suggestion.
  • Justification: For mass $m$ to be directly proportional to the period $T$ ($T \propto m$), the graph of $T$ against $m$ must be a straight line that passes through the origin $(0,0)$. From the plotted graph, the line of best fit is approximately horizontal, indicating that $T$ remains relatively constant as $m$ changes. If this line were extrapolated back to $m=0$, it would intersect the T-axis at approximately $T = 1.38 \text{ s}$, not 0. Therefore, $T$ is not directly proportional to $m$.