O Level Physics 5054 Paper 42, May/June 2023

method 1 The student measures: • the height $h$ of the cup • the diameter $D$ of the top of the cup • the diameter $d$ of the bottom of the cup. Fig. 1.1 shows a full-size diagram of the cup. Measure the height $h$, the diameter $D$ and the diameter $d$ of the cup in the diagram. $h=\text{......................................................... cm}$ $D=\text{......................................................... cm}$ $d=\text{......................................................... cm}$

Calculate the average diameter $d_{\mathrm{A}}$ of the cup using your readings from (a)(i) and the equation: $$d_{\mathrm{A}}=\frac{(D+d)}{2}$$ $d_{\mathrm{A}}=\text{................................................... cm}$

Calculate a value for the capacity $V_1$ of the cup using the equation: $$V_1=\frac{\pi d_{\mathrm{A}}^{2}h}{4}$$ $V_1={\text{.................................................. cm}}^3$

method 2 The student uses a length of string and a metre rule to determine the average circumference $C$ of the cup. The student: • wraps some of the string 5 times around the cup • measures the length $l$ of string used. $$l=87.9\text{ cm}$$ Calculate the average circumference $C$ of the cup. $C=\text{................................................... cm}$

Use your values of $h$ from (a)(i) and $C$ from (b)(i) to calculate a value for the capacity $V_2$ of the cup using the equation: $$V_2=\frac{C^{2}h}{4\pi }$$ $V_2={\text{................................................. cm}}^3$

method 3 The student: • fills a measuring cylinder with water, up to the $220{\text{ cm}}^3$ mark • pours water from the measuring cylinder into the cup until the cup is full • records the new reading $R$ on the measuring cylinder. Fig. 1.2 shows the new reading $R$. Write down the new reading $R$. $R={\text{.................................................. cm}}^3$

Determine the volume of water $V_3$ in the cup. Show your working. $V_3={\text{.................................................. cm}}^3$

All three methods of determining the capacity of the drinks cup give values which are approximate. State one reason why the volume calculated in method 2 and one reason why the volume calculated in method 3 are not accurate. method 2 .................................................................................................................................. ................................................................................................................................................... ................................................................................................................................................... method 3 .................................................................................................................................. ................................................................................................................................................... ...................................................................................................................................................

The student: • closes the switch • measures the potential difference $V_1$ across the resistors and the current $I_1$ in the circuit • opens the switch. The readings on the voltmeter and ammeter are shown in Fig. 2.2 and Fig. 2.3. Record the potential difference $V_1$ and the current $I_1$ shown in Fig. 2.2 and Fig. 2.3. $V_1=\text{........................................................... V}$ $I_1=\text{............................................................ A}$

Calculate the effective resistance $R_1$ of the combination of resistors using the equation: $$R_1=\frac{V_1}{I_1}$$ $R_1=\text{..................................................... }\mathrm{\Omega }$

Suggest why the switch is opened after the readings of potential difference and current have been taken.

The student: • rearranges the circuit so that the resistors are connected as shown in Fig. 2.4 • closes the switch • measures the potential difference $V_2$ and the current $I_2$ • opens the switch. The new readings are: $$V_2=2.8\text{ V}$$ $$I_2=0.88\text{ A}$$ Calculate the effective resistance $R_2$ of the combination of resistors using the equation: $$R_2=\frac{V_2}{I_2}$$ Record your answer on the answer line. Write down the value of $2R_2$ $R_2=\text{........................................................... }\mathrm{\Omega }$ $2R_2=\text{........................................................... }\mathrm{\Omega }$

If the resistors are identical, theory suggests that $R_1=2R_2$. Two quantities can be considered to be equal within the limits of experimental accuracy if their values are within 10% of each other. State whether the results indicate that the resistors are identical. Support your statement with a calculation. calculation statement .................................................................................................................................. .............................................................................................................................................

The student repeats the experiments in (a) and (b) but replaces the resistors with lamps. He obtains the following results: The effective resistance $R_3$ of the combination of lamps connected as in Fig. 2.1 is $5.2\mathrm{\Omega }$. The effective resistance $R_4$ of the combination of lamps connected as in Fig. 2.4 is $3.4\mathrm{\Omega }$. The teacher explains that the resistance of the lamp filaments changes due to a heating effect and therefore $R_3$ is not equal to $2R_4$. Suggest one observation that the student makes while doing the experiment that supports the teacher’s explanation.

The student extends the investigation using a different combination of the three lamps to the two combinations already used in (a) and (b). Complete the circuit diagram in Fig. 2.5 to show a third way of connecting three lamps between X and Y.

The illuminated triangular object is shown full size in Fig. 3.2. Measure and record the height $H$ of the triangular object. $H=\text{................................................... cm}$

The student: • switches on the lamp and places the lens a distance $u=20.0\text{ cm}$ from the triangular object • adjusts the position of the screen until a sharp, focussed image of the triangular object is formed on the screen. The image is shown full-size in Fig. 3.3. Measure the height $h$ of the image on the screen shown in Fig. 3.3 on page 11. $h=\text{.........................................................}$

Calculate the value of $\frac{1}{h}$. Give your answer to 2 significant figures. $\frac{1}{h}=\text{.........................................................}$ Add your values for $h$ and $\frac{1}{h}$ to Table 3.1.

The student repeats (b) for different values of $u$. He records all his readings in Table 3.1. Table 3.1 Complete the headers by adding appropriate units.

Calculate the remaining values of $\frac{1}{h}$ and add them to Table 3.1.

The screen is a square sheet of white card of side $10\text{ cm}$. Look at the data in Table 3.1 and suggest why the student does not use values of $u$ which are less than $20.0\text{ cm}$.

On the grid provided, plot a graph of $\frac{1}{h}$ on the y-axis against $u$ on the x-axis. Start both axes from the origin (0, 0). Draw the straight line of best fit.

Calculate the gradient $m$ of your line. Show all working and indicate on the graph the values you use. $m=\text{.........................................................}$

Calculate the focal length $f$ of the lens. Use your value of $H$ from (a) and the equation: $$f=\frac{1}{mH}$$ $f=\text{................................................... cm}$

When measuring the height of the image on the screen, the student’s hand and the ruler obstruct the light from the object and prevent it from reaching the screen. Suggest one improvement to the apparatus used by the student to overcome this problem.