Questions and Answers of Cambridge International AS & A Level Physics Coursebook

The volume of air inside a bottle affects its resonant frequency.a. What are the dependent and independent variables?b. Suggest one quantity to be controlled.c. How would you produce sounds of
Calculate:a. lg 10b. ln 10c. lg 100d. lg 5e. The antilogarithm to base 10 of 1 (i.e., find x where lg x = 1)f. The antilogarithm to base e of 0.5 (i.e., find x where ln x = 0.5).
In the expressions that follow, x and y are variables in an experiment. All the other quantities in the expressions are constants. In each case, state the graph you would plot to produce a straight
An experiment is being planned to measure how the resistance of a wire depends on the cross-sectional area of the wire. What are the independent and dependent variables? Suggest three quantities that
Each reading on a thermometer can be made with an uncertainty of ±0.5 °C.The thermometer is used to measure a temperature rise from 20 °C to 80 °C.What is the percentage uncertainty in the
What other graph can be plotted in Worked example 1, and how is its gradient used to find ρ? WORKED EXAMPLE 1 Plan an experiment to measure the resistivity p of glass, which is about 1010 2 m. You
The period T and the length l of a simple pendulum are measured to be T = 1.5 ± 0.1 s and l = 0.560 ± 0.001 m.The formula T = 2π√I/g is used to find the acceleration of free fall g.What is the
A nail is placed with its sharp end just touching a piece of wood. When a mass falls with a velocity v and hits the nail, it drives the nail into the wood. It is suggested that the depth d that the
The terminal velocity of an air bubble that rises in water is affected by the size of the bubble.a. What are the dependent and independent variables?b. Suggest a quantity to be controlled.c. How
The number 48 = 3 × 24. Calculate lg 48 and lg 3 + 4 lg 2. Why are they the same?
The count rate from a radioactive source emitting γ-radiation is inversely proportional to the square of the distance from the source. Sources emitting γ- radiation also emit α- and β-radiation
The size of a small toy balloon depends on atmospheric pressure.a. What are the dependent and independent variables?b. Suggest a quantity to be controlled.c. Draw a diagram of an apparatus to
The period of oscillation T of a small spherical mass supported by a length l of thread is given by the expression:T = 2π√I/gWhere g is the acceleration due to gravity. Design a laboratory
Quantities A and B have the following values: A = 3.0 ± 0.2 cm, B = 2.0 ± 0.1 cm. Find the value of the following expressions and their absolute uncertainties.a. ABb. A/Bc. A2d. A − Be. A2 −
The values of load shown in Table P2.4 are given without any indication of their uncertainties. Suggest a reason for this. Load / N Length of spring / cm Extension / cm 12.4 ± 0.2 0.0 1.00 14.0 ±
Explain how you draw the best fit line and the worst fit line on a graph and how you find the uncertainty in the intercept on the y-axis.a. The procedure to be followedb. The measurements to be
A student measures the radius r and the resistance R of several equal lengths of wire. The results are shown in Table P2.5. It is suggested that R and r are related by the equation:R = arbWhere a and
The resistance R of a light-dependent resistor (LDR) varies with the distance d from a very bright source of light. It is suggested that R and d are related by the formula R= kdn, where k and n are
A ruler with a small mass at one end is clamped at the other end, as shown, and oscillates up and down when plucked by hand.It is suggested that the period of oscillation T of the ruler is related to
A current-carrying coil produces a magnetic field. It is suggested that the magnetic field strength B at the centre of the coil is proportional to the current I in the coil. Design a laboratory
A bar magnet dropped into a coil induces an e.m.f. in the coil. It is suggested that E, the maximum induced e.m.f., is proportional to v, the speed of the magnet. Design a laboratory experiment to
A student has a number of different transformers of varying numbers of turns. An alternating input current to the transformer induces an output e.m.f. It is suggested that the output e.m.f. Vs is
The period T of a simple pendulum is related to its length l by the equation:T = 2π√I/gWhere g is the acceleration of free fall.a. A graph is plotted with T2 on the y-axis and l on the x-axis.
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 = kTn, where k and n are constants.a. A graph is plotted
Figure 28.20 shows another energy level diagram. In this case, energy is given in electron volts (eV). The list shows the energies of some photons:6.0 eV 9.0 eV 11 eV 20 eV 25 eV 34 eV 45
You are investigating how the current through a resistor depends on its resistance when connected in a circuit. You are given resistors of the following values:50Ω, 100Ω, 150Ω, 200Ω, 250Ω,
Quantity P has a fractional uncertainty p. Quantity Q has a fractional uncertainty q. What is the fractional uncertainty in P2/Q3 ?A. P − qB. P + qC. 2P − 3qD. 2P + 3q
Look at Figure P1.5. Draw similar diagrams to represent:a. A target where the holes are both precise and accurateb. A target where the holes are neither precise nor accurate.
The p.d. V across a wire of length l is given by the formula V = 4IpI/d2 where d is the diameter of the wire, ρ is the resistivity and there is a current I in the wire. Which quantity provides the
The position of the holes in Figure P1.5 represents attempts at measuring the position of the centre of the circle. Which one shows more random error and which shows more systematic error?
What is the uncertainty in the following sets of readings? All of them are written down to the smallest division on the instrument used in their measurement.a. 24.6, 24.9, 30.2, 23.6 cmb. 2.66, 2.73,
Figure P1.8 shows a lever-arm balance, initially with no mass in the pan and then with a standard 200 g mass in the pan. Explain what types of error might arise in using this equipment. standard 200
Electrical experiments usually involve the reading of meters such as the voltmeters shown.a. What is the reading shown by each voltmeter, and the uncertainty in each reading?b. The voltmeters show
Estimate the uncertainty when a student measures the length of a room using a steel tape measure calibrated in millimetres.
This apparatus can be used to test the hypothesis that T, the time taken for a ball to roll down a plane from rest, is related to the distance s by the formula T2 = ks, where k is a constant.The ball
Estimate the uncertainty when a girl measures the temperature of a bath of water using the thermometer in Figure P1.9.
An experiment explores the relationship between the period of a vibrating spring and the mass m in a pan holder. The student is instructed to set up the apparatus as shown here, with a mass of 200 g
A student is asked to measure the wavelength of waves on a ripple tank using a metre rule that is graduated in millimetres. Estimate the uncertainty in his measurement.
A student releases a toy car to roll down a ramp, as shown.The student measures the distance l from the middle of the car as it is released to the bottom of the ramp and the distance s travelled
Estimate the uncertainty when a student attempts to measure the time for a single swing of a pendulum.
This apparatus shows a resistor in some water.A student measures the rise in temperature θ of the water in 100 s using two different values of voltage.The student wrote:‘When the voltage was set
What is the average value and uncertainty in the following sets of readings? All are quoted to be consistent with the smallest scale division used.a. 20.6, 20.8b. 20, 30, 36c. 0.6, 1.0, 0.8, 1.2d.
The depth of water in a bottle is measured as 24.3 cm, with an uncertainty of 0.2 cm. (This could be written as (24.3 ± 0.2) cm.) Calculate the percentage uncertainty in this measurement.
The angular amplitude of a pendulum is measured as (35 ± 2)°.a. Calculate the percentage uncertainty in the measurement of this angle.b. The protractor used in this measurement was calibrated in
A student measures the potential difference across a battery as 12.4 V and states that his measurement has a percentage uncertainty of 2%. Calculate the absolute uncertainty in his measurement.
A ball is allowed to roll down a ramp from different starting points. Figure P1.10 shows the apparatus used. The ramp is placed at a fixed height above the floor. You are asked to measure the
a. Use your results from Question 13 to plot a graph of the square of the horizontal distance d2 (on the y-axis) against the height h (on the x-axis). Draw the best fit line.b. Determine the gradient
A student obtains the following data for two variables T and m (Table P1.5).The first value of T has an uncertainty of ±0.2 s. Do the results show that T is proportional to m? TIS / kg m 4.6 0.90
A student obtains the following values of two variables r and t (Table P1.6).The first value of r has an uncertainty of ± 0.2 cm, which is much greater than the percentage uncertainty in t. Do the
You measure the following quantities:A = (1.0 ± 0.4) mB = (2.0 ± 0.2) mC = (2.0 ± 0.5) m s−1D = (0.20 ± 0.01) sCalculate the result and its uncertainty for each of the following expressions.
A rifle bullet is photographed in flight using two flashes of light separated by a time interval of (1.00 ± 0.02) ms. The first image of the bullet on the photograph appears to be at a position of
Use a stopwatch and a metre rule to measure the average speed as an object falls from a table to the ground. What are the difficulties and how might they be reduced? Some of the suggestions will be
Hang a mass from a spring or from a rubber band. Use a stopwatch to time the mass as it oscillates up and down. Measure the time for just one oscillation, the time for 10 oscillations and the time
If you grip the bulb of a thermometer gently in your fingers, the reading rises to a new value. The reading will be different depending on whether you cover the bulb entirely or only partially with
Use the information given in the table in Question 9 about the Sun to show that the current temperature of the Universe matches with microwaves of wavelength 1 mm at peak intensity. Star Surface
The Tadpole galaxy has a recession speed of 9400 km s-1. Calculate the fractional change in the wavelength of the observed spectrum.
The fractional change in the wavelength of the observed light from a galaxy is 0.15; its redshift is 15 %. Calculate its recession speed. State any assumptions made.
A galaxy is at a distance of 9.5 × 1024 m from us and is moving away with a speed of 2.1 × 107 m s−1.a. Calculate the Hubble constant based on this data.b. Estimate the speed in km s−1 of a
The luminosity of the star Aldebaran is 520 times that of the Sun. The wavelength of light at peak intensity for Aldebaran is 740 nm and the wavelength of light at peak intensity for the Sun is 500
Use Wien's displacement law to complete the table. Write your answers to two significant figures.Copy this table. Star Surface temperature T/K Amax / nm Sun 5800 500 Polaris 6000 Canopus 7000 Gacrus
For a temperature of 5800 K, the wavelength at peak intensity of electromagnetic radiation is 500 nm. Calculate the surface temperature of a star with wavelength 350 nm at peak intensity.
a. Define radiant flux intensity.b. State the relationship between radiant flux intensity F and distance d from the centre of a star.c. Neptune is the farthest known planet from the Sun in the Solar
Light from a galaxy is passed through a diffraction grating. The diagram shows part of the emission spectrum.The strong emission spectral line has wavelength 662 nm.a. Calculate the energy of a
Use the data given in Figure 31.6 to show the validity of Wien’s displacement law for 5000 K and 4000 K. temperature T 5000 K 4000 K Wavelength / nm Amax 580 725 Intensity
a. A student conducted the experiment from Practical Activity 31.2. The results from the experiment are shown below:x = 300 mm d = 3 mmUse this data to estimate the diameter of the Sun.b. The actual
a. Define the luminosity of a star.b. A red giant is a star bigger than our Sun. Explain how the surface of a red giant star can be cooler than the Sun, yet have a luminosity much greater than the
The radiant flux intensity from a star measured at the Earth is 2.7 × 10−9 W m−2. The luminosity of the star is 1300 L⊙. Calculate the distance of this star from the Earth in metres.Where
a. State Hubble’s law.b. The recession speed v against distance d graph for some galaxies is shown.Determine the Hubble constant from this graph. Explain your answer.c. The Big Bang occurred some
This question is about Sirius and Arcturus. With the help of calculations and data from Table 31.1, show that Sirius is brighter than Arcturus.Where necessary, take:L⊙ = 3.83 × 1026 W1 ly ≈
A particular emission spectral line is measured in the laboratory to have a frequency of 7.3 × 1014 Hz.a. Calculate the wavelength of this spectral line in the laboratory.b. Calculate the observed
Use data from Table 31.1 to determine, to two significant figures:a. The distance of Sirius from the Earth in metres.b. The luminosity (in W) ofi. Canopusii. Vega.c. The radiant flux intensity
A group of astronomers have determined the radiant flux intensity F from a star and its distance d. The percentage uncertainty in F is 1.2 % and the percentage uncertainty in d is 2.5 %. What is the
The radiant flux intensity F of light from a lamp at a distance of 10 cm is 0.32 W m−2. Calculate F from the same lamp at a distance of 15 cm. State any assumption(s) you make.Where necessary,
Which statement is correct about radiant flux intensity?A. It depends on the area of the measuring device.B. It is measured in W m−2.C. It is the same as luminosity.D. It is the total radiant power
State two factors that affect radiant flux intensity from a star.Where necessary, take:L⊙ = 3.83 × 1026 W1 ly ≈ 9.5 × 1015 m
Explain why ultrasound cannot readily be used to examine the brain. Suggest one or more alternative scanning techniques that can be used for this.
The ultrasound image shown in Figure 30.25 clearly shows the baby’s skin and some bones. Explain why these show up clearly while softer organs inside its body do not. A 50 100 150 Energy of X-ray
a. i. With reference to PET scanning, explain the meaning of the term tracer.ii. Explain what is meant by the term line of response and how it is used to identify the precise site of cancerous
Two consecutive peaks in an ultrasound A-scan are separated by a time interval of 0.034 ms. Calculate the distance between the two reflecting surfaces. (Assume that the speed of sound in the tissue
Explain why an ultrasound B-scan, rather than X-rays, is used to examine a foetus.
Suggest the reason why, in PET scanning, it is important that the positron meets an electron within a very short distance from its point of emission.
Explain why the γ-rays produced in positron–electron annihilation must travel at 180° to each other.
Fluorine-18 decays by β+ emission. Write a nuclear equation to show this decay.
a. Calculate the energy released when a positron and an electron annihilate. (Mass of an electron = mass of a positron = 9.1 × 10−31 kg.)b. Calculate the frequency of the γ-rays emitted.c.
a. Outline the theory of the PET scanner.b. It is suggested that a scanner could be designed using the annihilation of a proton and an antiproton. Calculate:i. The energy released in the
Determine the fraction of the intensity of an ultrasound beam that is reflected when a beam is incident normally on a boundary between water and fat. SONCO
a. Explain what is meant by acoustic impedance and outline its role in the use of ultrasound scans.b. Brain tissue has a density of 1.04 × 103 kg m−3 and ultrasound travels at 1.58 × 103 m s−1
Calculate the acoustic impedance of muscle tissue. (Density = 1075 kg m−3; speed of sound = 1590 m s−1.)
a. An X-ray beam, containing X-rays with a variety of frequencies and that has an intensity of 4.0 × 105 W, is incident on an aluminium plate of thickness 5.0 cm. The average linear attenuation
Piezo-electric crystals have many applications other than in ultrasound scanning. For example, they are used in:a. Gas lighters (to produce a spark)b. Inkjet printers (to break up the stream of ink
Quartz is an example of a piezo-electric material. The speed of sound in quartz is 5700 m s−1.a. Calculate the wavelength of ultrasound waves of frequency 2.1 MHz in a quartz crystal.b. If the
This graph shows the spectrum of X-rays produced from an X-ray source.a. Describe the process by which:i. The three sharp peaks of high-intensity X-rays are producedii. The broad band of X-rays is
a. Explain, with the aid of a simple, labelled diagram, how X-rays are produced.b. Discuss the energy changes in the production of X-rays.
A patient with an injury to the skull, perhaps as a result of a road accident, is likely to undergo a CT scan. Explain why a CT scan is preferable to a conventional X-ray in a case like this.
State and explain two reasons why full-body CT scans are not offered for regular checking of healthy patients.
Suggest why a patient may be asked to hold his or her breath during a CT scan.
A transducer produces ultrasonic waves of frequency 800 kHz. The speed of sound in the crystal is 5200 m s−1. Calculate the optimum thickness for the crystal.
When low-energy X-rays are used, the attenuation coefficient μ is (roughly) proportional to the cube of the proton number Z of the absorbing material. Use the data in Table 30.2 to show that bone
For ultrasound of frequency 3.5 MHz, the acoustic impedance of muscle is 1.78 × 106 kg m−2 s−1, and that of soft tissue is 1.63 × 106 kg m−2 s−1.Calculate the percentage of the incident
The data in Table 30.2 shows how the attenuation coefficient μ depends on the energy of the X-rays in bone and muscle. When making a diagnostic X-ray image, it is desirable that bone should be

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