[Maximum number: 1]

The graph shows the relationship between two quantities p and q. The gradient of the graph is r and the intercept on the p axis is s.

Which of the following is the correct relationship between p and q ?

A

p=s q+r

B

p=r q+s

C

p=r q-s

D

p=r s+q

[Maximum number: 1]

Which of the following is a fundamental SI unit?

A

Ampere

B

Joule

C

Newton

D

Volt

[Maximum number: 1]

Which of the following is a fundamental SI unit?

A

Ampere

B

Joule

C

Newton

D

Volt

[Maximum number: 1]

What is the order of magnitude of the mass, in kg , of an apple?

A

$10^{-3}$

B

$10^{-1}$

C

$10^{+1}$

D

$10^{+3}$

[Maximum number: 1]

The sides of a square are measured to be $5.0 \pm 0.2 \mathrm{~cm}$ . Which of the following gives the area of the square and its uncertainty?

A

$25.0 \pm 0.2 \mathrm{~cm}^{2}$

B

$25.0 \pm 0.4 \mathrm{~cm}^{2}$

C

$25 \pm 2 \mathrm{~cm}^{2}$

D

$25 \pm 4 \mathrm{~cm}^{2}$

[Maximum number: 10]

The graph shows the plotted data for this experiment. Uncertainties in the data are not shown

(a)

Draw a best-fit line for the data.

[ 1 ]

(b)

It is hypothesized that the frequency f is inversely proportional to the height h.
By choosing two well separated points on the best-fit line that you have drawn in (a), show that this hypothesis is incorrect.

[ 4 ]

(c)

Another suggestion is that the relationship between f and h is of the form shown below, where k is a constant.

f=\frac{k}{h^{2}}

The graph shows a plot of f against $h^{-2}$ .

The uncertainties in $h^{-2}$ are too small to be shown.

[ 5 ]

(i)

Draw a best-fit line for the data that supports the relationship $f=\frac{k}{h^{2}}$ .

[ 2 ]

(ii)

Determine, using the graph, the constant k.

[ 3 ]

(a)

On the graph opposite, draw the line of best-fit for the data points.

[ 1 ]

(b)

Theory suggests that the relation between v and W is

v=k W^{3}

where k is a constant.
To test this hypothesis a graph of $v^{\frac{1}{3}}$ against W is plotted.

At $W=5.5 \mathrm{~N}$ the speed is $250 \pm 20 \mu \mathrm{~m} \mathrm{~s}^{-1}$ .
Calculate the uncertainty in $v^{\frac{1}{3}}$ for a load of 5.5 N .

[ 3 ]

(c)

(i)

Using the graph in (c), determine k without its uncertainty.

[ 4 ]

(ii)

State an appropriate unit for your answer to (d)(i).

[ 1 ]

(a)

(i)

On the graph opposite, draw error bars on the first and last points to show the uncertainty in v.

[ 1 ]

(ii)

On the graph opposite, draw the line of best-fit for the data points.

[ 1 ]

(b)

Theory suggests that the relation between v and W is

where k is a constant.
To test this hypothesis a graph of $v^{\frac{1}{3}}$ against W is plotted.

At $W=5.5 \mathrm{~N}$ the speed is $250 \pm 20 \mu \mathrm{~m} \mathrm{~s}^{-1}$ .
Calculate the uncertainty in $v^{\frac{1}{3}}$ for a load of 5.5 N .

[ 3 ]

(c)

(i)

Using the graph in (c), determine k without its uncertainty.

[ 4 ]

(ii)

State an appropriate unit for your answer to (d)(i).

A2. This question is about magnetic fields.

A long straight vertical conductor carries an electric current. The conductor passes through a hole in a horizontal piece of paper.

[ 1 ]

(a)

(i)

Draw the straight line that best fits the data.

[ 1 ]

(b)

Another student suggests that the relationship between t and h is of the form

t=k \sqrt{\frac{1}{h}}

where k is a constant.
To test whether or not the data support this relationship, a graph of $t^{2}$ against $\frac{1}{h}$ is plotted as shown below.

The best-fit line takes into account the uncertainties for all data points.

The uncertainty in $t^{2}$ for the data point where $\frac{1}{h}=10.0 \mathrm{~m}^{-1}$ is shown as an error bar on the graph.

[ 9 ]

(i)

State the value of the uncertainty in $t^{2}$ for $\frac{1}{h}=10.0 \mathrm{~m}^{-1}$ .

[ 1 ]

(ii)

Calculate the uncertainty in $t^{2}$ when $t=0.8 \pm 0.1 \mathrm{~s}$ . Give your answer to an appropriate number of significant digits.

[ 4 ]

(iii)

Use the graph to determine the value of k. Do not calculate its uncertainty.

[ 3 ]

(iv)

State the unit of k.

A2. This question is about the greenhouse effect.

The following data are available for use in this question:

[ 1 ]

[Maximum number: 6]

A1. Data analysis question.

A small sphere rolls down a track of constant length AB . The sphere is released from rest at A . The time t that the sphere takes to roll from A to B is measured for different values of height h.

A student suggests that t is proportional to $\frac{1}{h}$ . To test this hypothesis a graph of t against $\frac{1}{h}$ is plotted as shown on the axes below. The uncertainty in t is shown and the uncertainty in $\frac{1}{h}$ is negligible.

(a) (i) Draw the straight line that best fits the data.
(ii) State why the data do not support the hypothesis.
(b) Another student suggests that the relationship between t and h is of the form

t=k \sqrt{\frac{1}{h}}

where k is a constant.
To test whether or not the data support this relationship, a graph of $t^{2}$ against $\frac{1}{h}$ is plotted as shown below.

The best-fit line takes into account the uncertainties for all data points.

The uncertainty in $t^{2}$ for the data point where $\frac{1}{h}=10.0 \mathrm{~m}^{-1}$ is shown as an error bar on the graph.
(i) State the value of the uncertainty in $t^{2}$ for $\frac{1}{h}=10.0 \mathrm{~m}^{-1}$ .
(ii) Calculate the uncertainty in $t^{2}$ when $t=0.8 \pm 0.1 \mathrm{~s}$ . Give your answer to an appropriate number of significant digits.
(iii) Use the graph to determine the value of k. Do not calculate its uncertainty.
(iv) State the unit of k.