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IB Questionbank Physics 1

IB Measurements revision questions

1. Which of the following contains one fundamental and one derived unit?

A. ampere kilogram

B. ampere coulomb

C. joule newton

D. joule coulomb

(Total 1 mark)

2. Which of the following is equivalent to the joule?

A. N m2

B. N m–2

C. kg m s–2

D. kg m2 s

–2

(Total 1 mark)

3. The best estimate for the time it takes light to cross the nucleus of the hydrogen atom is

A. 10–23

s.

B. 10–20

s.

C. 10–15

s.

D. 10–7

s. (Total 1 mark)


4. The time taken for a stone dropped from rest to fall vertically through 16 m is 2.0 s. Based on

these measurements, what is the best estimate for the acceleration of free fall?

A. 4.0 m s–2

B. 8.0 m s–2

C. 9.8 m s–2

D. 10 m s–2

(Total 1 mark)

5. In an experiment to measure the acceleration of free fall at the surface of the Earth the following

results were obtained.

Acceleration of free fall / m s–2

7.69

7.70

7.69

7.68

7.70

The results are

A. accurate and precise.

B. inaccurate but precise.

C. accurate but imprecise.

D. inaccurate and imprecise. (Total 1 mark)


6. Which of the following will reduce random errors in an experiment?

A. Using an instrument having a greater precision

B. Checking the calibration of the instrument used

C. Checking for zero error on the instrument used

D. Repeating readings (Total 1 mark)

7. The current, I, through a resistor is measured with a digital ammeter to be 0.10 A. The

uncertainty in the calculated value of I2 will be

A. 1 %.

B. 2 %.

C. 5 %.

D. 20 %. (Total 1 mark)


8. The volume V of a cylinder of height h and radius r is given by the expression

V = r2h.

In a particular experiment, r is to be determined from measurements of V and h. The

uncertainties in V and in h are as shown below.

V 7

h 3

The approximate uncertainty in r is

A. 10 .

B. 5 .

C. 4 .

D. 2 . (Total 1 mark)

9. The density of a metal cube is given by the expression V

Mρ where M is the mass and V is the

volume of the cube. The percentage uncertainties in M and V are as shown below.

M 12

V 4.0

The percentage uncertainty in the calculated value of the density is

A. 3.0 .

B. 8.0 .

C. 16 .

D. 48 . (Total 1 mark)


10. The length of each side of a sugar cube is measured as 10 mm with an uncertainty of ±2 mm.

Which of the following is the absolute uncertainty in the volume of the sugar cube?

A. ±6 mm3

B. ±8 mm3

C. ±400 mm3

D. ±600 mm3

(Total 1 mark)

11. This question is about the electrical power available from a wind turbine.

The maximum electrical power generated by a wind turbine, Pout , was measured over a range of

incident wind speeds, vin.

The graph below shows the variation with vin of Pout. Uncertainties for the data are not shown.

(a) It is suggested that Pout is proportional to .inv

(i) Draw the line of best-fit for the data points. (1)


(ii) State one reason why the line you have drawn does not support this hypothesis.

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......................................................................................................................... (1)

(iii) The uncertainty in the power at 15 m s–1

is 5 . Draw an error bar on the graph to

represent this uncertainty. (2)

(b) The theoretical relationship between the available power in the wind, Pin, and incident

wind speed is shown in the graph below.


Using both graphs,

(i) determine the efficiency of the turbine for an incident wind speed of 14 m s–1

.

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(ii) suggest, without calculation, how the efficiency of the turbine changes with

increasing wind speed.

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(c) Outline one advantage and one disadvantage of using wind turbines to generate electrical

energy.

Advantage: ...................................................................................................

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Disadvantage: ...................................................................................................

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................................................................................................... (2)

(Total 12 marks)


12. Data analysis question.

The photograph below shows a magnified image of a dark central disc surrounded by concentric

dark rings. These rings were produced as a result of interference of monochromatic light.

The graph below shows how the ring diameter D varies with the ring number n.

The innermost ring corresponds to n = 1. The corresponding diameter is labelled in the

photograph. Error bars for the diameter D are shown.


(a) State one piece of evidence that shows that D is not proportional to n.

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...................................................................................................................................... (1)

(b) On the graph above, draw the line of best-fit for the data points. (2)

(c) Theory suggests that D2 = kn.

A graph of D2 against n is shown below. Error bars are shown for the first and last data

points only.


(i) Using the first graph, calculate the percentage uncertainty in D2, of the ring n = 7.

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(ii) Based on the second graph, state one piece of evidence that supports the

relationship D2 = kn.

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(iii) Use the second graph to determine the value of the constant k, as well as its

uncertainty.

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(iv) State the unit for the constant k.

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(Total 11 marks)


A student performs an experiment with a paper toy that rotates as it falls slowly through the air.

After release, the paper toy quickly attains a constant vertical speed as measured over a fixed

vertical distance.

The aim of the experiment was to find how the terminal speed of the paper toy varies with its

weight. The weight of the paper toy was changed by using different numbers of paper sheets in

its construction.


The graph shows a plot of the terminal speed v of the paper toy (calculated from the raw data)

and the number of paper sheets n used to construct the toy. The uncertainty in v for n = 1 is

shown by the error bar.

(a) The fixed distance is 0.75 m and has an absolute uncertainty of 0.01 m. The percentage

uncertainty in the time taken to fall through the fixed distance is 5 %.

(i) Calculate the absolute uncertainty in the terminal speed of the paper toy for n = 6.

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(ii) On the graph, draw an error bar on the point corresponding to n = 6. (1)


(b) On the graph, draw a line of best-fit for the data points. (1)

(c) The student hypothesizes that v is proportional to n. Use the data points for n = 2 and

n = 4 from the graph opposite to show that this hypothesis is incorrect.

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(d) Another student hypothesized that v might be proportional to n . To verify this

hypothesis he plotted a graph of v2 against n as shown below.

Explain how the graph verifies the hypothesis that v is proportional to n .

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(Total 11 marks)


14. This question is about liquid flow.

The diagram shows a storage container for liquids.

The container is filled from above. The distance between the base of the container and the

ground is h0.


The container, which is initially empty, is then filled at a constant rate. The height h of the

liquid surface above the ground is measured as a function of time t. The results of the

measurements are shown plotted below.

(a) Draw a best-fit line for the data. (1)

(b) It is hypothesized that h is directly proportional to t. State and explain whether this

hypothesis is correct for the periods

(i) t = 0 to t = 120 s.

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........................................................................................................................... (1)


(ii) t > 120 s.

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(c) Use data from the graph to determine the value of h0.

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(d) The area of the base of the container is 1.8 m2. Deduce that the volume of liquid entering

the storage container each second is approximately 0.02 m3 s

–1.

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(e) The container is completely filled after 850 s. Calculate the total volume of the container.

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...................................................................................................................................... (1)


(f) The empty container is now filled at half the rate in (d). Using the axes, sketch a graph to

show the variation of h with t in the range t = 0 to t = 900 s.

(2)

(Total 11 marks)


The frequency f of the fundamental vibration of a standing wave of fixed length is measured for

different values of the tension T in the string, using the apparatus shown.


In order to find the relationship between the speed v of the wave and the tension T in the string,

the speed v is calculated from the relation

v = 2 f L

where L is the length of the string.

The data points are shown plotted on the axes below. The uncertainty in v is ±5 m s–1

and the

uncertainty in T is negligible.

(a) Draw error bars on the first and last data points to show the uncertainty in speed v. (1)

(b) The original hypothesis is that the speed is directly proportional to the tension T.

Explain why the data do not support this hypothesis.

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...................................................................................................................................... (2)


(c) It is suggested that the relationship between speed and tension is of the form

v = k T

where k is a constant.

To test whether the data support this relationship, a graph of v2 against T is plotted as

shown below.

The best-fit line shown takes into account the uncertainties for each data point.

The uncertainty in v2 for T = 3.5 N is shown as an error bar on the graph.

(i) State the value of the uncertainty in v2 for T = 3.5 N.

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(ii) At T = 1.0 N the speed v = 27 ± 5 m s–1

. Calculate the uncertainty in v2.

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(d) Use the graph in (c) to determine k without its uncertainty.

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(Total 11 marks)

16. This question is about electrical resistance of the metal mercury.

The resistance R of a sample of mercury was measured as a function of the temperature T of the

sample. The sample was cooled and data points were taken at temperature intervals of 0.2 K.

The uncertainties in R and T are too small to be shown on the graph.

The hypothesis is that resistance is proportional to absolute temperature for temperatures greater

than 4.5 K.


(a) (i) Suggest whether the data supports the hypothesis.

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........................................................................................................................... (1)

(ii) Draw a line of best fit through the data. (2)

(b) State the value of R for which the rate of change of resistance of the sample with

temperature is least.

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(c) At a temperature TC the resistance suddenly becomes zero.

(i) Use the graph to determine the possible range of the temperature TC.

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(ii) State, to the correct number of significant figures, the value of TC and its

uncertainty.

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........................................................................................................................... (2)

(iii) Outline how the temperature TC could be measured more precisely.

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(d) Outline two reasons why you could not use the data to determine an accurate value for R

at room temperature.

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(Total 10 marks)


Gillian carried out an experiment to investigate the craters formed when steel balls are dropped

into sand. To try and find the relationship between the diameter of the crater and the energy of

impact of steel balls of the same diameter, she dropped a steel ball from different heights h into

sand and measured the resulting diameter d of the crater. The data are shown plotted below.

(a) The uncertainty in the measurement of d is ±0.40 cm; the uncertainty in h is too small to

be shown. Draw error bars for the data point (0.2, 0.047) and the data point (2.0, 0.10). (2)

(b) Draw a best-fit line for the data points. (2)


(c) The original hypothesis, made by Gillian, was that the diameter of the crater is directly

proportional to the energy of impact of the steel balls. Explain why the data does not

support this hypothesis.

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(d) Since Gillian’s data did not support her hypothesis, she researched to find alternative

hypotheses. She found that there are two theories used to predict a relationship between d

and h. In order to find which theory is best supported by the data, she processed the data

in two separate ways. The processed data are shown below.

(i) Draw a line of best-fit on each graph. (2)


(ii) State and explain which theory is best supported by the student’s data.

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(Total 11 marks)

18. This question is about electrical resistance.

The graph shows the variation with temperature T of the resistance R of an electrical

component.


(a) A student hypothesizes that the resistance is inversely proportional to the temperature.

Use data from the graph to show whether the hypothesis is supported.

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(b) A second student suggests that the relationship is of the form

lg R = a + T

b

where a and b are constants.

The student plots the graph below. Error bars have been included for the sake of clarity.


(i) Explain how the graph drawn could be used as evidence to support the student’s

suggestion.

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(ii) Use the graph to determine the constants a and b.

b: .......................................................................................................................

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a: .......................................................................................................................

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(iii) Using your answers to (b)(ii), determine a value for the resistance of the

component at a temperature of 260 K.

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(Total 11 marks)


19. Which of the following represents a scalar and a vector quantity?

Scalar Vector

A. electric potential electric potential gradient

B. electric potential gradient electric potential

C. electric potential electric potential difference

D. electric potential gradient electric field

(Total 1 mark)

20. Which of the following lists two scalar quantities?

A. emf, momentum

B. emf, weight

C. impulse, kinetic energy

D. magnetic flux, kinetic energy (Total 1 mark)

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