OCR A Level Physics B (Advancing) Fundamentals of physics November 2021 question paper H557/01

Which expression gives a quantity that can be expressed in watts?

A F s
where F is the force causing a body to move and s is its displacement

B I² R where I is the current in a conductor of resistance R

C m v
where m is the mass of a body moving with velocity v

D V I t
where V is the potential difference across a conductor and I is the current through it, which passes for time t

The camera in a smartphone contains a CCD detector of 1136 pixels × 640 pixels. Each pixel records in full RGB colour, encoded into three bytes of memory.

How much information is recorded in one image from the camera?

A 90.9 kbits

B 727 kbits

C 5.82 Mbits

D 17.4 Mbits

The following information is for use in questions 3 and 4.

A series of experiments on stretching a spring gave the data plotted in this graph. Analysis of the graph gives the information in the box.

Using the information in the box, which is the best estimate of the gradient of the graph, together with its uncertainty?

3.8 ± 0.7 cm N^–1 A

3.8 ± 1.4 cm N^–1 B

3.81 ± 0.35 cm N^–1 C

4 ± 2 cm N^–1 D

The following information is for use in questions 3 and 4.

A series of experiments on stretching a spring gave the data plotted in this graph. Analysis of the graph gives the information in the box.

Which is the best estimate of the unstretched length of the spring?

A 0.5 cm

B 2.6 cm

C 4.5 cm

D 7.5 cm

The following information is for use in questions 5 and 6.

The diagram shows a slide projector producing a magnified image on a distant screen. The slide is fixed in position and the lens and screen can be moved.

The slide is 4.0 cm from the lens and the screen is 10 m from the lens.

Which adjustments need to be made to produce a more magnified image?

The following information is for use in questions 5 and 6.

The diagram shows a slide projector producing a magnified image on a distant screen. The slide is fixed in position and the lens and screen can be moved.

The slide is 4.0 cm from the lens and the screen is 10 m from the lens.

The power of the projecting lens in dioptres, D is

A 0.040

B 0.071

C 25.0

D 25.1

The chart displays the strength and toughness of various materials.

Which type of material is weak and brittle?

A glasses

B metals and alloys

C polymers

D wood and wood products

The following three statements were made by students to explain the relationship between current I in an ohmic resistor and the p.d. V across it.

1 I is directly proportional to V

2 I and V are positively correlated

3 the ratio I / V becomes smaller as V increases

Which statements are correct?

A 1, 2 and 3 are correct

B only 1 and 2 are correct

C only 2 and 3 are correct

D only 1 is correct

The planet Mercury has an orbital period of 88.0 Earth days.

The mean angular velocity of its orbit, in rad s^–1, is

4.13 × 10^–7 A

8.26 × 10^–7 B

4.73 × 10^–5 C

4.96 × 10^–5 D

A car of mass 1100 kg moves up a hill of gradient 25°.

The force F is a component of the weight of the car. What is the value of F, to 2 significant figures?

A 4600 N

B 9800 N

C 12 000 N

D 26 000 N

The following information is for use in questions 11 and 12.

The questions are about the oscillation of an object suspended on a spring.

The graph shows the variation in displacement with time from its equilibrium position when the object is pulled down and released.

The maximum speed of the oscillating object is

0.08 m s^–1 A

0.24 m s^–1 B

0.39 m s^–1 C

39 m s^–1 D

The following information is for use in questions 11 and 12.

The questions are about the oscillation of an object suspended on a spring.

The graph shows the variation in displacement with time from its equilibrium position when the object is pulled down and released.

The mass of the oscillating object is 600 g.

The spring constant k of the spring is

14 N m^–1 A

18 N m^–1 B

56 N m^–1 C

14 000 N m^–1 D

Kirchhoff’s Second Law states that the sum of the potential differences around any closed loop in the circuit must be zero.

Here are three statements about the circuit above.

1 I₃ r < E

2 p.d. across R₁ = p.d. across R₂

3 p.d. across R₂ < p.d. across R₃

Which statements follow directly from Kirchhoff’s Second Law?

A 1, 2 and 3

B only 1 and 2

C only 2 and 3

D only 1

Kirchhoff’s First Law states that the sum of currents going into a junction is equal to the sum of currents coming out of that junction. Which conservation law is this equivalent to?

A conservation of charge

B conservation of energy

C conservation of mass

D conservation of momentum

A ball is thrown vertically upwards with an initial velocity of 24 m s^–1 and is caught by the thrower a 15 time t later.

To an appropriate number of significant figures, the time t is

A 2.4 s

B 2.45 s

C 4.89 s

D 4.9 s

A charged capacitor discharges through a resistor with the time constant = RC. What is the best explanation of the time constant ?

A is the time for the charge stored to become half of its initial value

B is the time for the current from the capacitor to become one-third of its initial value

C is the time for the energy stored to become half of its initial value D is the time for the p.d. across the capacitor to become of its initial value

What is the gain in potential when rising 1000 km above the surface of the planet Mars?

Mass of Mars = 6.4 × 10²³ kg Radius of Mars = 3400 km

2.9 × 10⁶ J kg^–1 A

9.7 × 10⁶ J kg^–1 B

1.3 × 10⁷ J kg^–1 C

2.9 × 10⁹ J kg^–1 D

A metal spike of mass 2.8 kg is dropped onto level ground from a height of 4.0 m, measured from the point of the spike. It penetrates into the ground a distance of 48 cm.

What is the mean force exerted on the spike by the ground as it penetrates?

A 2.3 N

B 82 N

C 230 N

D 260 N

A muon of rest energy = 106 MeV is travelling at a speed of 0.99 c. The total energy of the muon is

A 133 MeV

B 249 MeV

C 751 MeV

D 5330 MeV

The hydrogen atom can be modelled as an electron standing wave. One simple version has one ‘loop’ of the standing wave fitting in the diameter of the atom, as shown in the diagram.

The atom is ‘squeezed’ so that the diameter d becomes smaller.

Here are three statements about the change to the electron.

1 The electron momentum increases.

2 The electron kinetic energy increases.

3 The electron potential energy becomes more negative.

Which statements are correct?

A 1, 2 and 3 are correct

B only 1 and 2 are correct

C only 2 and 3 are correct

D only 1 is correct

The graph shows the variation of the charge on a capacitor with the potential difference across that capacitor.

The capacitor is initially uncharged and the p.d. is gradually increased. Use the graph to calculate the energy stored by the capacitor when the p.d. is 4.0 V.

A 0.012 J

B 0.024 J

C 12 J

D 24 J

The graph shows the variation of gravitational potential with radial distance r from the centre of the planet Mercury.

The mean radius of Mercury is 2440 km. The straight line drawn on the graph is the tangent to the curve at this value of r.

From the graph, the magnitude of the gravitational field strength at the surface of the planet is

0.0037 N kg^–1 A

3.7 N kg^–1 B

9.0 N kg^–1 C

18 N kg^–1 D

The distance from the Earth to an asteroid is measured by sending a radar pulse to the asteroid at a known time and recording the time when the return pulse is detected. The data from these measurements are given in the table.

The distance of the asteroid from Earth is

A 2.58 Gm

B 4.08 Gm

C 5.16 Gm

D 8.16 Gm

The diagram shows the refraction of a ray of light passing from water into glass.

The refractive index for light travelling from vacuum into water is 1.33.

Which of the following is the speed of light in glass, expressed to 3 significant figures?

1.99 × 10⁸ m s^–1 A

2.26 × 10⁸ m s^–1 B

2.40 × 10⁸ m s^–1 C

2.65 × 10⁸ m s^–1 D

The diagram shows a combination of three resistors connected to a 6.0 V power supply of negligible internal resistance.

A voltmeter connected across resistor R reads 3.0 V. What is the resistance of resistor R ?

A 50

B 100

C 150

D 200

The graph shows the binding energy per nucleon for different nuclides.

From the graph, what is the energy released when one nucleus of²³⁵₉₂U undergoes fission into one nucleus of¹⁴⁴₅₆Ba, one nucleus of⁸⁹₃₆Kr and two neutrons?

A 9.3 MeV

B 170 MeV

C 1200 MeV

D 1800 MeV

The diagram shows the path of two alpha particles, each of initial kinetic energy 4.0 MeV, as they are scattered by a gold nucleus.

Alpha particle 1 approaches head-on towards the gold nucleus and is repelled back along its own path, with a closest distance of separation from the nucleus being d. Alpha particle 2 follows the path shown, with a closest distance of separation from the nucleus being 2 d at the point X.

What is the kinetic energy of alpha particle 2 at the point X ?

A 0.0 MeV

B 2.0 MeV

C 3.0 MeV

D 4.0 MeV

The STM image below shows an open ring of silver atoms.

Use the scaled STM image to estimate the diameter of a silver atom.

The diagram shows a 2.0 ms interval of a waveform that is to be digitised. The waveform contains noise at the level V_noise ≈ 0.4 mV.

Explain why the sampling frequency should be at least 25 kHz.

Suggest and explain the number of bits per sample you would use to digitise this waveform.

The figures below show evidence of the Hubble law (v = H₀d where v is the velocity of the galaxy relative to Earth and d is the distance of the galaxy from Earth).

Fig. 33a shows Hubble’s original galactic red-shift data (1929). Fig. 33b shows evidence from supernovae red-shift data (1998).

Three of the nearer galaxies in Fig. 33a have a negative velocity.

Suggest and explain the effect this has on the wavelength shift for these galaxies.

Show from the lines of best fit that the best estimate for the Hubble constant H₀ was more than eight times (× 8) larger in 1929 than in 1998.

Show that the data from Fig. 33b indicate that the ‘big bang’ happened more than 10 billion years ago.

1 Mpc (megaparsec) = 3.1 × 10²² m

In radiotherapy, ‘seeds’ of radioactive material are implanted in tumours to eliminate cancer cells. Each seed contains a quantity of the isotope¹²⁵I with half-life 60 days and initial activity 8.5 MBq.

Show that the number of atoms of¹²⁵I atoms initially present in one seed is about 6 × 10¹³ (a)

Seeds are implanted into cancer masses and remain there for many half-lives.

Suggest why implanting many seeds throughout a 50 gram cancer may be better than implanting one larger seed at its centre.

The graph shows how the Boltzmann factor f varies with temperature T for a process requiring activation energy E.

Use the graph to estimate the temperature T when E = kT for this process.

Explain why the process completes at this temperature, but may occur at a significant

This question considers the internal resistance of chemical cells.

* Explain how you would practically measure the internal resistance of a 1.5 V cell.

Include in your answer a circuit diagram of components with appropriate values, and your

method of what readings to take and how to analyse them to find the internal resistance.

A lithium-ion rechargeable cell has an e.m.f. of 4.2 V. The cell is rated at 9 A h (Ampere × hours).

Show that the unit A h is a unit of charge.

The graph shows the potential difference of the cell against time as it completely discharges at a constant load current of 4.5 A.

The internal resistance of the fully charged cell is 0.02 . The internal resistance rises to 0.27 when the cell is fully discharged.

The resistance scale is at the right side of the graph and the initial and final values are marked with +.

Add a curve to the graph which shows how the internal resistance changes with time.

Assume that any p.d. dropped by the cell is due to its internal resistance.

Estimate the number of moles of lithium Li + ions that are needed to store the amount of (iii) charge delivered by this cell.

one mole = 6.0 × 10²³ ions

State what is meant by a friction compensated runway.

* Trolley A has mass 0.90 kg and trolley B has mass 0.30 kg. Trolley A travels down the runway at constant speed into the stationary trolley B. Repelling magnets fixed to the trollies ensure they do not make physical contact.

Both trollies are attached to ticker-tapes onto which 50 dots per second are printed. The ticker-tapes of the collision are shown in Fig. 37.2. The time between printed dots is 0.02 s. The tapes have been divided into ‘5-tick strips’ before and after the collision representing time intervals of 0.10 s.

Analyse the ticker-tapes to compare the motion of the two trollies. Include discussion of the conservation of momentum and kinetic energy and of the force on each trolley during the collision.

You may assume the collision impulse lasts for 0.060 s. The tape images are life-size.

A high-pressure fire hose has a tapered nozzle as shown in Fig. 37.3.

The nozzle is reduced from diameter D₁ = 75 mm to diameter D₂ = 25 mm. Water enters the nozzle at point E at velocity v₁ and leaves at point F with velocity v₂.

Explain why v₂ = 9 v₁.

The hose can deliver 0.020 m³ s^–1 of water.

Calculate the velocity v₁ of water entering the nozzle.

=........ m s^–1 v₁

Show that the force on the nozzle is about 700 N.

Use 0.020 m³ s^–1 is equivalent to 20 kg s^–1 for water

This question is about the electric field strength E near to a proton leading to the Bohr model for the hydrogen atom.

State what the area under the graph between two r values represents and make an estimate of its value between the marked r values 52 and 160 pm.

Show that the kinetic energy of the electron in orbit is where k is the electric force constant = 1 / 4_o.

Accelerating electrons emit electromagnetic radiation.

Suggest why Bohr had to introduce the quantisation principle of allowed energy levels into his model atom.

Explain why the rotor will turn clockwise when coil 1 pole is a S and coil 2 pole is a N and coil 3 is off.

In Fig. 39.1b the rotor has rotated 90° aligning between coils 3 and 1. Coil 2 is off, coil 1 pole is a S and coil 3 pole is a N.

Explain each of the following design features of the motor:

1 The stator is made of iron. 2 The stator is laminated (made of layers of iron separated by thin layers of insulator). 3 The air gap between the rotor magnet and the coil poles is kept as small as possible.

For this motor, suggest how to control each of the following.

1 The rate of rotation of the rotor. 2 The force that acts to turn the rotor.

Write in the box below each graph of Fig. 40 the proportionality relationship shown.

Combine all the proportionality relationships into one equation using the Boltzmann constant k.

For one mole of gas at standard temperature and pressure (STP):

T = 273 K P = 101 kPa V = 22.4 litres.

Calculate the value of the Boltzmann constant to 3 significant figures using this data.

Show your working to 4 significant figures.

Boltzmann constant =........ J K^–1

Calculate the root mean square speed for helium gas at 300 K.

molar mass for helium = 4.0 × 10^–3 kg

speed =........ m s^–1

A typical speed for an air molecule at 300 K is about 4 × 10³ m s^–1. (ii)

Explain why the scent from an air freshener may take several minutes to reach across a room of still air.

This question is about neutron stability and the -decay process. This table shows the properties of the free particles that combine to form atoms.

Particle	Symbol	Mass / u	Half-life t1/2 / s
electron	–10e	0.000549	stable
proton	11p	1.007276	stable
neutron	10n	1.008665	650

Calculate the maximum energy available when a free neutron decays into a proton and a

1 u = 931 MeV

The -particles from neutron decay have a spectrum of energies up to this maximum value as shown in Fig. 41.1.

State why the beta particles are emitted with a range of energies.

Estimate the number of neutrons that would decay in one second from a sample of 10⁴ (iii) free neutrons.

A down quark has electric charge of – e and an up quark has electric charge + . State what is happening in terms of quarks during -decay.