Learn Extracted exam questions A-Level Physics 9702 Physics November 2025 Question Paper 53
9702 Physics November 2025 Question Paper 53
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On a bench, a steel ball of radius $r$ is used to compress a spring by a distance $x$. The ball is held at rest in this position, as shown in Fig. 1.1.
The ball is released and rolls along the bench. At a fixed point P, the ball has speed $v$. The speed of the ball at P is determined using \textbf{one} light gate connected to a timer.
Several steel balls of different radii are available.
It is suggested that $v$ is related to $r$ by the relationship
where $k$ is the spring constant of the spring, $\rho$ is the density of the steel, and $Y$ and $n$ are constants.
Plan a laboratory experiment to test the relationship between $v$ and $r$.
Draw a diagram showing the arrangement of your equipment.
Explain how the results could be used to determine values for $Y$ and $n$.
In your plan you should include:
\begin{itemize} \item the procedure to be followed \item the measurements to be taken \item the control of variables \item the analysis of the data \item any safety precautions to be taken. \end{itemize}
A student investigates light from different galaxies.
Fig. 2.1 shows the lines in the absorption spectrum from a distant galaxy.
The wavelength of one of the lines in the absorption spectrum is $\lambda$. The wavelength of this spectral line in the laboratory is $\lambda_0$.
The observations of the same spectral line are repeated for different galaxies.
The student determines the distance $d$ of each galaxy from the Earth.
It is suggested that $\lambda$ and $d$ are related by the equation
where $c$ is the speed of light in free space and $H$ is the Hubble constant.
A graph is plotted of $\lambda$ on the $y$-axis against $\frac{d}{c}$ on the $x$-axis.
Determine expressions for the gradient and $y$-intercept.
gradient = \hrulefill $y$-intercept = \hrulefill
Values of $d$ and $\lambda$ are given in Table 2.1.
\begin{center} \textbf{Table 2.1}
\begin{tabular}{|c|c|c|} \hline $d / 10^{21}\text{ km}$ & $\frac{d}{c} / 10^{15}\text{ s}$ & $\lambda / \text{nm}$ \ \hline $0.48 \pm 0.12$ & & $658.4$ \ \hline $1.04 \pm 0.12$ & & $661.2$ \ \hline $1.45 \pm 0.12$ & & $664.2$ \ \hline $1.80 \pm 0.12$ & & $665.7$ \ \hline $2.85 \pm 0.12$ & & $672.4$ \ \hline $3.75 \pm 0.12$ & & $678.2$ \ \hline \end{tabular} \end{center}
The value of $c$ is $3.00 \times 10^5\text{ km}\,\text{s}^{-1}$.
Calculate and record values of $\frac{d}{c} / 10^{15}\text{ s}$ in Table 2.1. Include the absolute uncertainties in $\frac{d}{c}$.
Plot a graph of $\lambda / \text{nm}$ against $\frac{d}{c} / 10^{15}\text{ s}$. Include error bars for $\frac{d}{c}$.
Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.
Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.
gradient = \hrulefill
Determine the $y$-intercept of the line of best fit. Include the absolute uncertainty in your answer.
$y\text{-intercept} =$ \hrulefill
Using your answers to \textbf{(a)}, \textbf{(c)(iii)} and \textbf{(c)(iv)}, determine the values of $\lambda_0$ and $H$. Include appropriate units.
$\lambda_0 =$ \hrulefill $H =$ \hrulefill
Hubble's law suggests that the age $T$ of the universe is related to $H$ by
Determine a value for $T$. Include the absolute uncertainty in your answer.
$T =$ \hrulefill $\text{ s}$