O Level Physics 5054 Paper 42, Oct/Nov 2024

Measure the height $h$ of the test-tube in Fig. 1.1 to the nearest $0.1\text{ cm}$. $h=\text{................................................... cm}$

Measure the external diameter $d$ of the test-tube in Fig. 1.1. $d=\text{................................................... cm}$

The student uses a ruler and two wooden blocks to help obtain an accurate answer for the height $h$. Fig. 1.2 shows how the student uses the wooden blocks. Explain why it is important for the student to ensure that the blocks are parallel to one another.

The shape of the test-tube is approximately a cylinder. Calculate the external volume $V_{\text{E}}$ of the test-tube using the equation: $$V_{\text{E}}=0.79d^{2}h$$ $V_{\text{E}}={\text{.................................................. cm}}^3$

The student: • fills the test-tube to the top with water • pours the water from the test-tube into a measuring cylinder. Fig. 1.3 shows the measuring cylinder. Record the reading $V_{\text{I}}$ on the measuring cylinder. This is the internal volume of the test-tube. $V_{\text{I}}={\text{.................................................. cm}}^3$

Calculate the volume $V_{\text{G}}$ of the glass in the test-tube using the equation: $$V_{\text{G}}=V_{\text{E}}-V_{\text{I}}$$ $V_{\text{G}}={\text{.................................................. cm}}^3$

Suggest one source of inaccuracy in measuring the internal volume of the test-tube $V_{\text{I}}$.

The student uses a balance to measure the mass $m$ of the test-tube. Fig. 1.4 shows the reading on the balance. Record $m$ to the nearest gram. $m=\text{...................................................... g}$

Use your results from (g)(i) and (e) to calculate the density $\rho$ of the glass from which the test-tube is made using the equation: $$\rho =\frac{m}{V_{\text{G}}}$$ Give the unit for your answer. $\rho =\text{............................}$ unit = $\text{..................}$

The student: • connects a voltmeter across the $270\mathrm{\Omega }$ resistor between points X and Y • closes the switch • records the voltmeter reading of the potential difference $V_{\text{XY}}$ in the top row of Table 2.1 • opens the switch. On Fig. 2.1, draw the symbol for a voltmeter connected to measure the potential difference $V_{\text{XY}}$ across the $270\mathrm{\Omega }$ resistor.

Fig. 2.2 shows the voltmeter reading of the potential difference $V_{\text{XY}}$ when the voltmeter is connected across the $270\mathrm{\Omega }$ resistor. Record $V_{\text{XY}}$ in Table 2.1.

The student: • disconnects the voltmeter from points X and Y • reconnects the voltmeter across the LED between points Y and Z • closes the switch • records the voltmeter reading of the potential difference $V_{\text{YZ}}$ in the correct row of Table 2.1 • opens the switch. Calculate the value of $(V_{\text{XY}}+V_{\text{YZ}})$ for the $270\mathrm{\Omega }$ resistor. Record your answer in Table 2.1.

The current $I$ in the circuit can be calculated using the equation: $$I=\frac{V_{\text{XY}}}{R}$$ where $R=270\mathrm{\Omega }$. Calculate $I$. Record your answer in Table 2.1.

The resistance $R_{\text{LED}}$ of the LED can be calculated using the equation: $$R_{\text{LED}}=\frac{V_{\text{YZ}}}{I}$$ Calculate $R_{\text{LED}}$. Record your answer in Table 2.1.

The student repeats the procedure in (a) and (b), replacing the $270\mathrm{\Omega }$ resistor, first with a $470\mathrm{\Omega }$ resistor and then with a $560\mathrm{\Omega }$ resistor. The student’s results are shown in Table 2.1, but the value of $V_{\text{XY}}$ for the $560\mathrm{\Omega }$ resistor is missing. Calculate $V_{\text{XY}}$ and record your answer in Table 2.1 on page 6.

As the resistance between terminals X and Y changes, the current in the circuit changes. Examine the results in Table 2.1. Describe how the change in current affects: $(V_{\text{XY}}+V_{\text{YZ}})$

$R_{\text{LED}}$.

Another student assembles a circuit using the circuit diagram shown in Fig. 2.1. This student finds that, when the switch is closed, the LED does not light up. The student tests the components and finds that the power source is producing an e.m.f., and that none of the other components are broken. Suggest the error this student has made while assembling the circuit.

Name and draw the symbol of a single device that can be used to change the current in the circuit without the need to connect different resistors across the terminals X and Y in the circuit in Fig. 2.1. name of device ......................................................................................................................... symbol for device

The student: • arranges the apparatus as shown in Fig. 3.1 • places a white screen approximately $30\text{ cm}$ from the lens • adjusts the position of the screen until a sharp image of a window in the laboratory, a few metres distant from the lens, is formed on the screen. Measure and record, in centimetres to the nearest $0.1\text{ cm}$, the distance $x$ on Fig. 3.1 from the lens to the screen. $x=\text{................................................... cm}$

The distance $x$ shown on Fig. 3.1 is drawn to a scale of one-third full size. Use your answer from (a)(i) to calculate the actual distance from the lens to the screen. This distance is the focal length $f$ of the lens. $f=\text{................................................... cm}$

The student: • rearranges the apparatus as shown in Fig. 3.2 • switches on the lamp • places the lens a distance $u=20.0\text{ cm}$ from an illuminated triangular object • adjusts the position of the screen until a sharp image of the triangular object is formed on the screen • measures the image distance $v$ from the lens to the screen. $$v=60.5\text{ cm}$$ Calculate the values of $(u+v)$ and $uv$. Record your values of $(u+v)$ and $uv$ to an appropriate number of significant figures on the answer lines and in the first row of Table 3.1. $(u+v)=\text{...............................................................}$ $uv=\text{...............................................................}$

The student repeats (b) for values of $u$ between $u=25.0\text{ cm}$ and $u=55.0\text{ cm}$. The student’s results are shown in Table 3.1. Add appropriate units to the headers of the last two columns.

On the grid provided in Fig. 3.3, plot a graph of $uv$ on the $y$-axis against $(u+v)$ on the $x$-axis. You do not need to start either axis from the origin $(0,0)$. Draw the straight line of best fit.

Calculate the gradient of the line. Indicate on the graph the points you use. Show all your working. gradient = .........................................................

Two quantities can be considered to be the same within the limits of experimental accuracy if their values are within $10\mathrm{\%}$ of each other. The gradient of your line calculated in (e) is numerically equal to the focal length $f$ of the lens in $\text{cm}$. Compare your value of $f$ obtained in (a)(ii) with the value of the gradient obtained in (e). State if your two values can be considered to be the same. Support your statement with a calculation. calculation statement ..................................................................................................................................

When measuring the object and image distances with a metre rule, it is important to avoid line-of-sight (parallax) errors. State how the student avoids parallax errors when doing the experiment.

Describe a technique that the student uses to make sure that the image on the screen is as sharply focused as possible.