9702 Physics November 2025 Question Paper 31

Slide the double spring and the two single springs onto the longer wooden rod.

Set up the apparatus as shown in Fig. 1.1.

\begin{itemize} \item Using the shorter wooden rod, hang mass $m$ as shown in Fig. 1.2. \item Gently place the hook of the mass hanger near the centre of the shorter rod. \item Carefully adjust the position of the mass hanger until the shorter rod is approximately parallel to the bench, as shown in Fig. 1.2. \item Gently pull the mass down through a short distance. When released, the mass will oscillate. \item Take measurements to determine the period $T_2$ of the oscillations. \end{itemize}

$T_2 =$ \hrulefill

\begin{itemize} \item Remove the mass. \end{itemize}

Vary $m$. For each value of $m$, determine $T_1$ and $T_2$. Repeat until you have five sets of values of $m$, $T_1$ and $T_2$. Do not use values of $m$ less than 200g.

Record your results in a table. Include values of $\sqrt{T_1}$ and $\sqrt{T_2}$ in your table.

It is suggested that the quantities $\sqrt{T_2}$ and $\sqrt{T_1}$ are related by the equation

where $P$ and $Q$ are constants.

Using your answers in \textbf{(d)(iii)}, determine the values of $P$ and $Q$. Give appropriate units.

P = \hrulefill Q = \hrulefill

You have been provided with two pieces of paper.

The width of a piece of paper is the length $w$ of the shorter side, as shown in Fig. 2.1.

\begin{itemize} \item Select the smaller piece of paper. \item Measure and record $w$. \end{itemize}

$w =$ \hrulefill cm

\begin{itemize} \item Roll the paper into a cylinder and use two paper clips to hold the paper in place, as shown in Fig. 2.2. \item The diameter of the cylinder is $d$, as shown in Fig. 2.2. \newline Adjust the paper and paper clips until $d$ is as close as possible to 7.0 cm. \item Measure and record $d$. \end{itemize}

$d =$ \hrulefill cm

Set up the apparatus as shown in Fig. 2.3.

\begin{itemize} \item Slide the loop of the upper spring onto the wooden rod. \item Hang a mass of 200g from the lower spring. \item Adjust the height of the boss until the bottom of the mass is approximately 10cm above the bench. \item Place the paper cylinder so that the middle of the cylinder is under the mass, as shown in Fig. 2.3. \item The length of the springs is $y$, as shown in Fig. 2.3. \end{itemize}

By adjusting the height of the boss, lower the mass to squash the middle of the paper cylinder until the bottom of the mass is 2.5 cm above the bench, as shown in Fig. 2.4.

Using the \textbf{larger} sheet of paper, repeat \textbf{(a)}, \textbf{(b)(i)}, \textbf{(c)(i)} and \textbf{(c)(ii)}.

$w =$ \hrulefill cm

$d =$ \hrulefill cm

$y =$ \hrulefill cm

$p =$ \hrulefill cm

$(y - p) =$ \hrulefill cm

It is suggested that the relationship between $w$, $y$ and $p$ is

where $k$ is a constant.

It is suggested that the percentage uncertainty in the values of $k$ is 10%.

Using this uncertainty, explain whether your results support the relationship in (e).