O Level Physics 5054 Paper 41, May/June 2024

method 1 The student: • places six small glass balls by the side of a metre rule as shown in Fig. 1.1 • makes sure that there are no gaps between the balls. Take readings on the metre rule of the positions of points A and B shown in Fig. 1.1. Give your readings to the nearest 0.1 cm. position of point A = .......................................................... cm position of point B = .......................................................... cm

The length $l$ on Fig. 1.1 is the distance between points A and B. The average diameter $d$ of one ball can be found using the equation: $$l=6d$$ Use your answers to (a)(i) to calculate the length $l$ and diameter $d$. Give your answers to the nearest 0.1 cm. $l=$ .......................................................... cm $d=$ .......................................................... cm

The average volume $V$ of one glass ball using this method, is given by the equation: $$V=\frac{3.14d^3}{6}$$ Calculate $V$. $V=$ .................................................. ${\text{cm}}^3$

method 2 • The student pours water into a measuring cylinder. The volume of water in the measuring cylinder $V_1$ is shown in Fig. 1.2. Write down the reading $V_1$. $V_1=$ .................................................. ${\text{cm}}^3$

• The six glass balls are carefully added to the water in the measuring cylinder. The new reading on the measuring cylinder $V_2$ is shown in Fig. 1.3. The volume $V_{\text{T}}$ of the six balls is given by $$V_{\text{T}}=V_2-V_1\mathrm{.}$$ Calculate $V_{\text{T}}$. Show your working. $V_{\text{T}}=$ .................................................. ${\text{cm}}^3$

Calculate the average volume $V$ of one ball using this method. Give your answer to the nearest $0.1{\text{ cm}}^3$. $V=$ .................................................. ${\text{cm}}^3$

Suggest whether method 1 or method 2 gives the more accurate value for the volume of the ball. Explain your answer. method giving more accurate value .......................................................................................... explanation ............................................................................................................................... ................................................................................................................................................... ...................................................................................................................................................

The student now uses the six glass balls to find the average mass of one glass ball using a small beaker and a top pan (electronic) balance. Describe the method the student uses.

The student: • pours $100{\text{ cm}}^3$ of hot water into a $250{\text{ cm}}^3$ beaker • uses a thermometer to take the temperature of the water at time $t=0\text{ s}$. The thermometer reading at time $t=0\text{ s}$ is shown in Fig. 2.1. Record the temperature of the water at time $t=0\text{ s}$ in Table 2.1.

The student then records the temperature $\theta$ of the water every $30\text{ s}$ for $240\text{ s}$. The results are recorded in Table 2.1. Before taking each temperature reading, the student carefully stirs the water in the beaker. Explain why.

Calculate the average cooling rate $C_1$ of the water for the first $90\text{ s}$ of the experiment. Use the readings in Table 2.1 and the equation: $$C_1=\frac{{\theta }_0-{\theta }_{90}}{t}$$ where ${\theta }_0$ is the temperature of the water at $0\text{ s}$, ${\theta }_{90}$ is the temperature at $90\text{ s}$ and $t$ is the time of $90\text{ s}$. Give the unit for $C_1$. $C_1=$ .................................. unit ...............

Calculate the average cooling rate $C_2$ of the water for the final $90\text{ s}$ of the experiment. Use the equation: $$C_2=\frac{{\theta }_{150}-{\theta }_{240}}{t}$$ where ${\theta }_{150}$ is the temperature of the water at $150\text{ s}$, ${\theta }_{240}$ is the temperature of the water at $240\text{ s}$ and $t$ is the time of $90\text{ s}$. $C_2=$ .................................. unit ...............

Compare your values of $C_1$ and $C_2$. Explain any difference in these values.

The student repeats the procedure described in (a)(i) but this time he places the $250{\text{ cm}}^3$ beaker inside a larger beaker containing iced water. The arrangement is shown in Fig. 2.2. The student reads the temperature $\theta$ of the hot water, records the reading and immediately starts the stop-watch. Table 2.2. shows the temperature $\theta$ at times $t=0\text{ s}$, $30\text{ s}$, $60\text{ s}$, and $90\text{ s}$. Calculate the average cooling rate of the hot water for the $90\text{ s}$. Use the readings in Table 2.2 and the equation: $$C_3=\frac{{\theta }_0-{\theta }_{90}}{t}$$ $C_3=$ .................................. unit ...............

Describe how $C_3$ differs from $C_1$. Explain your answer.

The recorded readings show that this experiment is not a valid comparison of $C_1$ and $C_3$. By referring to the results recorded in Table 2.1 and Table 2.2, explain why this is not a valid comparison.

State one other variable that should be kept constant to make a valid comparison.

Measure and record distance $x$ on Fig. 3.1. $x=$ .................................................... cm

Fig. 3.1 is drawn to a scale of one fifth full size. Use your answer to (a)(i) to calculate the actual object distance $u$ from the lens. $u=$ .................................................... cm

Deduce the image distance $v$, the distance from the lens to the screen when a clear image is seen. $v=$ .................................................... cm

Fig. 3.2 shows the shape of the illuminated object and Fig. 3.3 shows the image seen on the screen. Describe two differences between the illuminated object and its image on the screen. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ...................................................................................................................................................

The student moves the screen away from the illuminated object and repeats the procedure for values of $D=70.0\text{ cm}$, $80.0\text{ cm}$, $90.0\text{ cm}$ and $100.0\text{ cm}$. Table 3.1 shows the values recorded. Add your values for $u$ and $v$ from (a)(ii) and (a)(iii) to Table 3.1 on page 12. Complete Table 3.1 by calculating the value of $(u\times v)$ for each value of $D$. Give your answers to 3 significant figures.

Use the grid provided in Fig. 3.4 on page 13 to plot a graph of $(u\times v)\mathrm{/}{\text{cm}}^2$ on the y-axis against $D\mathrm{/}\text{ cm}$ on the x-axis. You do not need to start your axes at the origin (0,0). Draw the straight line of best fit.

The focal length $f$ of the lens is numerically equal to the gradient of the line. Calculate the gradient of the line. Show all working and indicate on your graph in Fig. 3.4 the values you use. $f=$ .................................................... cm

The lens manufacturer states that the focal length of the lens is $15.0\text{ cm}\pm 10\mathrm{\%}$. Decide, with a calculation, whether your value of $f$ agrees with this statement and tick the box that shows your answer. calculation: [ ] My value for $f$ agrees with the manufacturer’s statement. [ ] My value for $f$ does not agree with the manufacturer’s statement.