A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

 Values of $r \& R$ measured in an experiment are given in Table.

Copy and complete the table by calculating and recording values of $\ln (r/\mathrm{mm})$ and $\ln (R/\Omega )$ and include the absolute uncertainties in $\ln (r/\mathrm{mm})$

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

 Plot a graph of $\ln (r/\mathrm{mm})$ against $\ln (R/\Omega )$. Include error bars for $\ln (r/\mathrm{mm})$.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

 Draw the line of best fit and a worst acceptable straight line on your graph.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

Determine the gradient of the line of best fit. Include the uncertainty in your answer.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

Determine the value of $b$ according to the best fit line.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

Determine the value of $a$ and its uncertainty.

Make a checklist of all the important points that you are likely to forget or which led to you losing marks in any of the exercises.

Each reading on a thermometer can be made with an uncertainty of $\pm 0.5°\mathrm{C}$. The thermometer is used to measure a temperature rise from $20°\mathrm{C}$ to $80°\mathrm{C}$. What is the percentage uncertainty in the measurement of this temperature rise?

The period $T$ and the length $l$ of a simple pendulum are measured to be $T=1.5\pm 0.1 \mathrm{s}$ and $l=0.560\pm 0.001 \mathrm{m}$.

The formula $T=2\pi \sqrt{\frac{l}{g}}$ is used to find the acceleration of free fall $g$. What is the best estimate of the uncertainty in the value of $g$ ?