David Sang and Graham Jones Solutions for Chapter: Practical Skills at A Level, Exercise 8: EXAM-STYLE QUESTIONS

The period $T$ of a simple pendulum is related to its length $l$ by the equation:

$T=2\pi \sqrt{\frac{l}{g}}$

Where $g$ is the acceleration of free fall.

A student measures the time $t$ for $10$ oscillations for different lengths $l$. This table shows her data.

Using the value of $g$ and its uncertainty, calculate the value of $t$ when the length $l$ is $0.900 \mathrm{m}$. Include the absolute uncertainty in your answer.

Readings are taken of the resistance $R$ of a thermistor at different temperatures $T$. It is suggested that the relationship between $R$ and $T$ is $R=k{T}^n$, where $k$ and $n$ are constants. A graph is plotted with $\log \left(R\right)$ on the y-axis and $\log \left(T\right)$ on the x-axis. State the value of the gradient and the y-intercept in terms of $k$ and $n$.

Readings are taken of the resistance $R$ of a thermistor at different temperatures $T$. It is suggested that the relationship between $R$ and $T$ is $R=k{T}^n$, where $k$ and $n$ are constants. Values for $T$ and $R$ are shown in the given table:

Complete the table and include absolute uncertainties in $\log \left(\mathrm{R}/\mathrm{\Omega }\right)$.

Readings are taken of the resistance $R$ of a thermistor at different temperatures $T$. It is suggested that the relationship between $R$ and $T$ is $R=k{T}^n$, where $k$ and $n$ are constants.

Plot a graph of $\log (\mathrm{R}/\mathrm{\Omega })$ against $\log (\mathrm{T}/\mathrm{K})$.

Readings are taken of the resistance $R$ of a thermistor at different temperatures $T$. It is suggested that the relationship between $R$ and $T$ is $R=k{T}^n$, where $k$ and $n$ are constants.

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

Readings are taken of the resistance $R$ of a thermistor at different temperatures $T$. It is suggested that the relationship between $R$ and $T$ is $R=k{T}^n$, where $k$ and $n$ are constants.

Determine the gradient of your line of best fit and the uncertainty in your value.

Readings are taken of the resistance $R$ of a thermistor at different temperatures $T$. It is suggested that the relationship between $R$ and $T$ is $R=k{T}^n$, where $k$ and $n$ are constants.

Determine the $y$ -intercept of your graph (this is where the $x$ -value, in this case, $\lg (T/\mathrm{K})$, is zero). Give the uncertainty in your value.

Readings are taken of the resistance $R$ of a thermistor at different temperatures $T$. It is suggested that the relationship between $R$ and $T$ is $R=k{T}^n$, where $k$ and $n$ are constants.

Determine values for $n$ and $k$ and the uncertainties in your answers.