A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(d) Describe four sources of uncertainty or limitations of the procedure for this experiment.

protractor, $30 \mathrm{cm}$ ruler, metre rule, micrometer screw gauge, calipers, newton-meter balance, measuring cylinder, thermometer, stopwatch, ammeter and voltmeter.

Can you suggest, for each instrument in the list, what is its range and its smallest scale division, and suggest a simple experimental problem in using it?

You are investigating how the current through a resistor depends on its resistance when connected in a circuit. You are given resistors of the following values:

$50\Omega ,100\Omega ,150\Omega ,200\Omega ,250\Omega ,300\Omega ,350\Omega ,400\Omega ,450\Omega ,500\Omega$

You are asked to take measurements with just six of these resistors. Which six resistors would you choose? Explain your choice.

Look at Figure. Draw similar diagrams to represent:

The left-hand diagram represents readings that are precise but not accurate; the right-hand diagram represents readings that are accurate but without precision.

 A target where the holes are both precise and accurate

This apparatus shows a resistor in some water.

A student measures the rise in temperature $\theta$ of the water in $100 \mathrm{s}$ using two different values of voltage.

The student wrote:

'When the voltage was set at $6.0 \mathrm{V}$, the rise in temperature of the water in $100 \mathrm{s}$ was $14.5°\mathrm{C}$. The voltmeter reading decreased by about $0.2 \mathrm{V}$ during the experiment, and so the final voltmeter reading was $5.8 \mathrm{V}$. 'The reading fluctuated from time to time by about $0.2 \mathrm{V}$. The smallest scale division on the thermometer was $1°\mathrm{C}$, but I could read it to $0.5°\mathrm{C}$. I did not have time to repeat the reading.

'When the voltage was set at $12.0 \mathrm{V}$, the rise in temperature in $100 \mathrm{s}$ was $51.0°\mathrm{C}$ and the voltage was almost the same at the end, but fluctuated by about $0.2 \mathrm{V}$ ''

(a) Estimate the percentage uncertainty in the measurement of the first voltage.

This apparatus shows a resistor in some water.

A student measures the rise in temperature $\theta$ of the water in $100 \mathrm{s}$ using two different values of voltage.

The student wrote:

'When the voltage was set at $6.0 \mathrm{V}$, the rise in temperature of the water in $100 \mathrm{s}$ was $14.5°\mathrm{C}$. The voltmeter reading decreased by about $0.2 \mathrm{V}$ during the experiment, and so the final voltmeter reading was $5.8 \mathrm{V}$. 'The reading fluctuated from time to time by about $0.2 \mathrm{V}$. The smallest scale division on the thermometer was $1°\mathrm{C}$, but I could read it to $0.5°\mathrm{C}$. I did not have time to repeat the reading.

'When the voltage was set at $12.0 \mathrm{V}$, the rise in temperature in $100 \mathrm{s}$ was $51.0°\mathrm{C}$ and the voltage was almost the same at the end, but fluctuated by about $0.2 \mathrm{V}$ ''

(b) It is suggested that $\theta$ is related to $V$ according to the formula $\theta =k{V}^2$, where $k$ is a constant.

(ii) Justify the number of significant figures you have given for your value of $k$.

This apparatus shows a resistor in some water.

A student measures the rise in temperature $\theta$ of the water in $100 \mathrm{s}$ using two different values of voltage.

The student wrote:

'When the voltage was set at $6.0 \mathrm{V}$, the rise in temperature of the water in $100 \mathrm{s}$ was $14.5°\mathrm{C}$. The voltmeter reading decreased by about $0.2 \mathrm{V}$ during the experiment, and so the final voltmeter reading was $5.8 \mathrm{V}$. 'The reading fluctuated from time to time by about $0.2 \mathrm{V}$. The smallest scale division on the thermometer was $1°\mathrm{C}$, but I could read it to $0.5°\mathrm{C}$. I did not have time to repeat the reading.

'When the voltage was set at $12.0 \mathrm{V}$, the rise in temperature in $100 \mathrm{s}$ was $51.0°\mathrm{C}$ and the voltage was almost the same at the end, but fluctuated by about $0.2 \mathrm{V}$ ''

(b) It is suggested that $\theta$ is related to $V$ according to the formula $\theta =k{V}^2$, where $k$ is a constant.

(iii) Explain whether the results support the suggested relationship.