O Level Physics 5054 Paper 41, Oct/Nov 2023

Fig. 1.2 shows a scale marked on the side of the dropping pipette. Describe the technique the student uses to put $1.0{\text{ cm}}^3$ of water into the dropping pipette.

The student observes the wavefront travel outwards from the centre of the plate and then reflect from the rim back to the centre. Fig. 1.3 is a side view of the wavefront as it spreads out across the diameter $D$ of the plate. The student uses a stop-watch to measure the time $t$ taken for the wavefront to travel outwards from the centre of the plate and then back to the centre. Fig. 1.4 shows three readings for time $t$. Use the stop-watch readings in Fig. 1.4 to determine an accurate value for $t$. Show your working and give your answer to a suitable number of significant figures. $t=\text{...................................................... s}$

The speed of the wavefront can be calculated using the equation: $$\text{speed}=\frac{\text{distance}}{\text{time}}$$ Fig. 1.3 is drawn to a scale of 1:2. It is half the size of the plate used in the experiment. Calculate the speed of the wavefront using your answer from (b)(i) and a measurement taken from Fig. 1.3. $$\text{speed}=\text{................................................ cm/ s}$$

Identify two causes of uncertainty in this experiment. 1 ........................................................................................................................................ 2 ........................................................................................................................................

Suggest one improvement that could be made to this experiment.

Fig. 2.2 shows the voltmeter when the flying lead is connected to the resistance wire at the $100.0\text{ cm}$ mark on the rule and the switch closed. Read the voltage shown in Fig. 2.2 and record the reading in Table 2.1 on page 6.

Calculate the current $I$ for each length $L$ shown in Table 2.1 using the equation $I=\frac{V}{10}$. Record your answers in Table 2.1. Calculate values of $\frac{1}{I}$ for each length $L$ shown in Table 2.1 and record your answers in Table 2.1. Write the units in the top row of the table.

On the grid on page 7, plot a graph of $\frac{1}{I}$ on the y-axis against $L$ on the x-axis. Start both axes at the origin (0,0).

Draw the straight line of best fit. Extend this line to intercept the y-axis.

Determine the gradient $G$ and y-intercept $c$ of this line. Show clearly on the graph the values you choose and show your working. gradient $G$ = ............................................................... y-intercept $c$ = ...............................................................

Theory suggests that: $$R_{\text{w}}=\frac{1000G}{c}$$ where $R_{\text{w}}$ is the resistance of the wire. Use your answers in (b)(iii) to determine $R_{\text{w}}$. Show your working. $$R_{\text{w}}=\text{..................................................... }\mathrm{\Omega }$$

Describe briefly how to use the apparatus in Fig. 3.1 to determine the diameter of the glass ball. Draw a labelled diagram of the arranged apparatus to help your explanation.

The student uses the glass ball to make an indentation in a piece of modelling clay. Fig. 3.2 shows the apparatus used. A $300\text{ g}$ mass with weight $F_1=3.0\text{ N}$ is placed on a wooden strip directly above the glass ball. The mass is left in place for one minute and then removed. The student repeats the experiment with the ball on a different part of the clay and the $300\text{ g}$ mass hanging at the end of the wooden strip as shown in Fig. 3.3. The lengths $x$ and $y$ in Fig. 3.3 are shown to a scale of 1:5. The actual lengths $X$ and $Y$ are five times larger. Measure $x$ and $y$ on Fig. 3.3. $x\text{ on Fig. 3.3}=\text{.................. mm}$ $y\text{ on Fig. 3.3}=\text{.................. mm}$

Calculate the actual lengths $X$ and $Y$ in metres to the nearest mm. actual length $X$ = .................. m actual length $Y$ = .................. m

Calculate the force $F_2$, exerted on the clay by the ball, using the equation: $$F_2=\frac{3Y}{X}$$ Show your working. $$F_2=\text{..................................................... N}$$

When the ball presses into the surface of the clay, it makes a small circular mark. This mark is called an indentation. Fig. 3.4 shows the indentations made by the glass ball in the surface of the clay. The indentations are drawn full size. The smaller indentation is made by the mass positioned as shown in Fig. 3.2. The larger indentation is made by the mass positioned as shown in Fig. 3.3. Measure and record the diameter of the smaller indentation $d_1$ and the diameter of the larger indentation $d_2$. $$d_1=\text{........................................................ mm}$$ $$d_2=\text{........................................................ mm}$$

The graph in Fig. 3.5 shows the relationship between the diameter of the indentation and the surface area of the modelling clay inside the indentation for this glass ball. On Fig. 3.5, plot the data shown in Table 3.1. Table 3.1

On Fig. 3.5, draw the best-fit curve.

Use Fig. 3.5 to determine the surface areas $A_1$ and $A_2$ of the modelling clay inside the indentations with diameters $d_1$ and $d_2$ recorded in (c). Show on your graph how you arrive at your answers. Area $A_1$ of the indentation with the diameter $d_1={\text{..................................................... mm}}^2$ Area $A_2$ of the indentation with the diameter $d_2={\text{..................................................... mm}}^2$

Another student claims that: $$A_2=k{A}_1\text{and}{F}_2=k{F}_1$$ where $k$ is a constant, $F_1=3.0\text{ N}$ and $F_2$ is your answer to (b)(iii). Using your values of $F_2$, $A_1$ and $A_2$ from (b)(iii), and (d)(iii), calculate two values of $k$. Record your answers to a suitable number of significant figures. first value of $k$ = ............................................................... second value of $k$ = ...............................................................

Values of $k$ are assumed to be the same within the limits of experimental accuracy if they are within 10% of each other. Explain whether these results show that the student’s claim is correct.

Students in another laboratory obtain different values of $A_1$ and $A_2$ using the same arrangement of the apparatus. Identify two variables that should be controlled to ensure similar values of $A_1$ and $A_2$ when using modelling clay. 1 ................................................................................................................................................ 2 ................................................................................................................................................