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\begin{tabular}{|c|c|c|c|c|c|}
\hline
[tex]L ( cm )[/tex] & [tex]T_1[/tex] & [tex]T_2[/tex] & Mean [tex]T[/tex] & [tex]T^2[/tex] \\
\hline
140.00 & 49.50 & 49.00 & 49.25 & 6.0639 \\
120.00 & 46.00 & 44.5 & 45.25 & 5.1179 \\
100.00 & 41.00 & 40.50 & 40.75 & 4.1514 \\
80.00 & 36.00 & 36.6 & 36.3 & 3.2942 \\
60.00 & 32.50 & 32.0 & 32.25 & 2.6001 \\
40.00 & 26.60 & 26.22 & 26.41 & 1.7437 \\
20.00 & 20.66 & 20.60 & 20.63 & 1.0639 \\
\end{tabular}

Questions:
a. From the table, plot a graph of [tex]L[/tex] against [tex]T^2[/tex].

b. Determine the shape of the graph.

c. State two sources of error.

Sagot :

GinnyAnswer
Sure! Let's go through the questions step-by-step.

### Part (a): Plotting a Graph of [tex]\( L \)[/tex] Against [tex]\( T^2 \)[/tex]

We'll start by extracting the values from the table and plotting the graph.

#### Given Data:
1. [tex]\( L \)[/tex] (cm): [tex]\( [140.00, 120.00, 100.00, 80.00, 60.00, 40.00, 20.00] \)[/tex]
2. [tex]\( T^2 \)[/tex] (seconds[tex]\(^2\)[/tex]): [tex]\( [6.0639, 5.1179, 4.1514, 3.2942, 2.6001, 1.7437, 1.0639] \)[/tex]

To create a plot:
1. Plot [tex]\( T^2 \)[/tex] values along the x-axis.
2. Plot [tex]\( L \)[/tex] values along the y-axis.

Ensure that you label the axes appropriately. The x-axis will be titled "T^2 (seconds[tex]\(^2\)[/tex])" and the y-axis will be titled "L (cm)".

### Part (b): Shape of the Graph

When you plot [tex]\( L \)[/tex] against [tex]\( T^2 \)[/tex], observe the relationship between the two variables. In the context of a simple pendulum, the period [tex]\( T \)[/tex] is related to the length [tex]\( L \)[/tex] of the pendulum by the equation:

[tex]\[ T = 2\pi\sqrt{\frac{L}{g}} \][/tex]

where [tex]\( g \)[/tex] is the acceleration due to gravity. This equation implies a quadratic relationship [tex]\( L \propto T^{2} \)[/tex].

Given this relationship, the graph of [tex]\( L \)[/tex] against [tex]\( T^2 \)[/tex] should be a straight line. This suggests that as [tex]\( T^2 \)[/tex] increases, [tex]\( L \)[/tex] increases linearly, confirming a direct proportional relationship.

### Part (c): Sources of Error

When conducting experiments involving measurements such as time and length, there are common sources of error. Two possible sources of error in this experiment are:

1. Human Reaction Time: There can be inaccuracies in timing measurements because the time intervals are being recorded manually. When starting and stopping a stopwatch, human reaction delay can cause inconsistencies.

2. Length Measurement Accuracy: The lengths could have been measured with a ruler or a measuring tape. Small errors in alignment or reading off the scale can introduce inaccuracies.

In summary:

1. Plot a graph of [tex]\( L \)[/tex] against [tex]\( T^2 \)[/tex] as described.
2. Shape of the graph: The graph should be a straight line, indicating a linear relationship.
3. Sources of error:
- Human reaction time in timing measurements.
- Inaccuracies in length measurements.

Feel free to sketch this graph on graph paper or use graphing software to visualize the data accurately!
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