What is question 1232/3 of the Kigumo Subcounty Cluster Exam, which is a Physics exam lasting 2 1/2 hours?

Question 1

Step 1: State the aim.
To determine the diameter of a given wire using micrometer screw gauge.

Measure the diameter $d$ of the wire.

$d = least count \times reading$

Step 2: Record readings.
Zero error = 0.
Main scale reading = 2.5 mm, circular scale coinciding = 23 divisions.
Least count = 0.01 mm.

Substitute:
$d = 2.5 + 0.01 \times 23 = 2.73 \, mm$

Step 3: Graph.
(Sketch a straight line graph of load vs. extension for wire, passing through origin.)

Diameter = 2.73 mm

2.73 mm

Question 2

Step 1: Aim: To verify Hooke's law.
Hooke's law: $F = k x$, where $F$ is load, $x$ is extension, $k$ spring constant.

Step 2: Table of readings.
\begin{tabular}{|c|c|c|} \hline
Load (N) & Extension (cm) & $x$ (m) \ \hline
0 & 0 & 0 \
2 & 1.2 & 0.012 \
4 & 2.4 & 0.024 \
... & ... & ... \ \hline
\end{tabular}

Step 3: Plot graph of load vs extension.
Graph: Straight line through origin, slope = $k$.

From graph, slope = $\frac{\Delta F}{\Delta x} = \frac{10}{0.05} = 200 \, \text{N/m}$.

Spring constant $k = 200 \, \text{N/m}$.

k = 200 N/m

Question 3

Step 1: Aim: To determine acceleration due to gravity $g$ using simple pendulum.

Period $T = 2\pi \sqrt{\frac{l}{g}}$.

$g = \frac{4\pi^2 l}{T^2}$

Step 2: Record length $l$ and time $t$ for 20 oscillations.

Sample: $l = 0.50$ m, $t = 14.2$ s.

$T = \frac{14.2}{20} = 0.71 \, s$

Step 3: Calculate $g$.
$T^2 = (0.71)^2 = 0.5041 \, s^2$

$g = \frac{4 \times \pi^2 \times 0.50}{0.5041} = 9.81 \, m/s^2$

Step 4: Graph of $T^2$ vs $l$.
$y = \frac{4\pi^2}{g} x$

Slope = $\frac{4\pi^2}{g} = 4.05 \, s^2/\text{m}$.

$g = \frac{4\pi^2}{4.05} = 9.8 \, m/s^2$

g = 9.8 m/s^{2}