[Maximum number: 1]

The density of a metal sphere is determined using a digital caliper and a mass balance.

The digital caliper is used to measure the diameter D of the sphere by placing the sphere in the jaws of the digital caliper. This reading is shown.

The sphere is then removed and another reading is taken immediately afterwards with the jaws closed.

(a)

State one way in which the procedure for the measurement of D can be improved using the same digital caliper.

[ 1 ]

[Maximum number: 1]

A student attaches one end of a copper wire to an oscillator operating at a fixed frequency. The other end of the wire passes over a pulley to weights that hang vertically. The first harmonic standing wave is established by using the slider to change the length of the wire. The procedure is repeated for different weights.

The mass m of the weights and the wavelength $\lambda$ of the wave are related by

m=\frac{\mu f^{2}}{g} \lambda^{2}

where $\mu$ is a constant, f is the frequency of the wave and $g=9.8 \mathrm{~ms}^{-2}$ .

(a)

The graph shows the data obtained by the student, plotted to show the variation of m with $\lambda^{2}$ .

[ 1 ]

(i)

Suggest a possible reason for the systematic error.

[ 1 ]

[Maximum number: 2]

A student investigates the oscillation of a horizontal rod hanging at the end of a vertical string. The diagram shows the view from above.

The student starts the rod oscillating and measures the largest displacement for each cycle of the oscillation on the scale and the time at which it occurs. The student begins to take measurements a few seconds after releasing the rod.

The graph shows the variation of displacement x with time t since the release of the rod. The uncertainty for t is negligible.

(a)

The student hypothesizes that the relationship between x and t is $x=\frac{a}{t}$ where a is a constant.

To test the hypothesis x is plotted against $\frac{1}{t}$ as shown in the graph.

[ 2 ]

(i)

Suggest the range of values of t for which the hypothesis may be assumed to be correct.

[ 2 ]

[Maximum number: 2]

In an experiment to measure the acceleration of free fall a student ties two different blocks of masses $m_{1}$ and $m_{2}$ to the ends of a string that passes over a frictionless pulley.

The student calculates the acceleration a of the blocks by measuring the time taken by the heavier mass to fall through a given distance. Their theory predicts that $a=g \frac{m_{1}-m_{2}}{m_{1}+m_{2}}$ and this can be re-arranged to give $g=a \frac{m_{1}+m_{2}}{m_{1}-m_{2}}$ .

(a)

There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain,

[ 2 ]

(i)

the advantage with reference to the magnitude of the acceleration that is obtained.

[ 2 ]

(a)

On looking at the results the student suggests that $\varepsilon$ could be inversely proportional to d. He proceeds to multiply each d value by the corresponding value of $\varepsilon$ .

[ 2 ]

(i)

Explain why this procedure can be used to disprove the student's suggestion but it cannot prove it.

[ 2 ]

[Maximum number: 1]

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

(a)

State one reason why the results of the experiment could not be used to predict the natural frequency of oscillation for girders of height 50 m .

[ 1 ]

[Maximum number: 1]

The graph shows a set of experimental results to determine the density of oil. The results have systematic errors and random errors.

Using the information on the graph, what can be said about the measurements used to find the density of oil?

Systematic errors

Random errors

small

large

small

large

[Maximum number: 3]

A student measures the refractive index of the glass of a microscope slide.

He uses a travelling microscope to determine the position $x_{1}$ of a mark on a sheet of paper. He then places the slide over the mark and finds the position $x_{2}$ of the image of the mark when viewed through the slide. Finally, he uses the microscope to determine the position $x_{3}$ of the top of the slide.

The table shows the average results of a large number of repeated measurements.

(a)

After the experiment, the student finds that the travelling microscope is badly adjusted so that the measurement of each position is too large by 0.05 mm .

[ 3 ]

(i)

State the name of this type of error.

[ 1 ]

(ii)

Outline the effect that the error in (b)(i) will have on the calculated value of the refractive index of the glass.

[ 2 ]

[Maximum number: 2]

An experiment is conducted to measure the specific heat capacity of water. A mass of water is placed in a glass beaker and energy is transferred from an electric heater.

electric heater

The data collected are:

Mass of water $=(0.250 \pm 0.002) \mathrm{kg}$
Change in temperature of the water $=(14.0 \pm 0.5)^{\circ} \mathrm{C}$
Energy transferred from the electric heater $=(16000 \pm 300) \mathrm{J}$

(a)

Outline one source of systematic error in the experiment and its effect on the calculated value of the specific heat capacity of water. provided.

[ 2 ]

[Maximum number: 2]

In an experiment to measure the specific latent heat of vaporization of water $L_{\mathrm{v}}$ , a student uses an electric heater to boil water. A mass m of water vaporizes during time $t . \quad L_{\mathrm{v}}$ may be calculated using the relation

L_{\mathrm{v}}=\frac{V I t}{m}

where V is the voltage applied to the heater and I the current through it.

(a)

A student suggests that to get a more accurate value of $L_{\mathrm{v}}$ the experiment should be performed twice using different heating rates. With voltage and current $V_{1}, I_{1}$ the mass of water that vaporized in time t is $m_{1}$ . With voltage and current $V_{2}, I_{2}$ the mass of water that vaporized in time t is $m_{2}$ . The student now uses the expression

L_{v}=\frac{\left(V_{1} I_{1}-V_{2} I_{2}\right) t}{m_{1}-m_{2}}

to calculate $L_{\mathrm{v}}$ . Suggest, by reference to heat losses, why this is an improvement. provided.

[ 2 ]

Question 1

Question 1(b)

Question 1

Question 1(b)

Question 1(b)(iii)

Question 1

Question 1(c)

Question 1(c)(ii)

Question 1

Question 1(b)

Question 1(b)(i)

Question A1

Question A1(b)

Question A1(b)(i)

Question A1

Question A1(d)

Question 2

Question 2

Question 2(b)

Question 2(b)(i)

Question 2(b)(ii)

Question 2

Question 2(b)

Question 2

Question 2(c)