Physics questions and solutions

Browse original practice and official past-paper questions. Each question has its own link, with its source and worked solution.

498 questions · Page 17 of 21

1. Q171 · Original practice · 5 marks
   The graph gives the signed magnetic flux per turn of an $80$-turn stationary coil. Positive flux is out of the page. The graph is piecewise linear. Define positive EMF as driving conventional current counterclockwise when viewed on the page; this is the circulation associated with the outward normal.
   Electromagnetism
2. Q172 · Original practice · 5 marks
   A coil has $120$ turns, each of area $8.00\times10^{-3}\,\mathrm{m^2}$, in a uniform $0.400\,\mathrm T$ field. The coil rotates so its area normal changes from parallel to the field to $60.0^\circ$ to the field in $0.200\,\mathrm s$.
   Electromagnetism
3. Q173 · Original practice · 7 marks
   A conducting rod of length $0.400\,\mathrm m$ slides right at $3.00\,\mathrm{m\,s^{-1}}$ on parallel rails. A uniform field $0.250\,\mathrm T$ points into the page. The closed circuit has resistance $2.00\,\Omega$, and rail/rod resistance and friction are negligible. Motion is maintained at constant speed.
   Electromagnetism
4. Q174 · Original practice · 7 marks
   An ideal transformer has $600$ primary turns and $30$ secondary turns. It is connected to a $240\,\mathrm V$ rms AC supply. A connected load draws $2.00\,\mathrm A$ rms from the secondary.
   Electromagnetism
5. Q175 · Original practice · 6 marks
   A spacecraft's crew measures its length as $120\,\mathrm m$. A laboratory measures its length along its direction of motion as $72.0\,\mathrm m$. A clock fixed on the spacecraft records $0.600\,\mu\mathrm s$ between two ticks.
   Special relativity
6. Q176 · Original practice · 8 marks
   A beam of muons moves toward the ground at $0.980c$. Their mean proper lifetime is $2.20\,\mu\mathrm s$. They are created $3.00\,\mathrm{km}$ above the ground in the ground frame. Use $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$ and ignore changes in speed.
   Special relativity
7. Q177 · Original practice · 7 marks
   A light clock has two mirrors separated vertically by $0.600\,\mathrm m$ in its own frame. A pulse travels from the lower mirror to the upper mirror and back to the lower mirror. The clock moves horizontally at $0.600c$ relative to a laboratory. Its vertical separation is unchanged. Use $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$. The diagram shows the laboratory…
   Special relativity
8. Q178 · Original practice · 6 marks
   A train moves right at $0.600c$ relative to the ground. At ground time $t=0$, its rear and front are at $x=-300\,\mathrm m$ and $x=+300\,\mathrm m$, respectively. Light pulses are emitted inward from both ends simultaneously in the ground frame. An observer at the train's centre is then at $x=0$ and keeps moving with the train. Use…
   Special relativity
9. Q179 · Original practice · 5 marks
   A proton has relativistic momentum three times its classical value $m_0v$ at the same speed. Use $m_0=1.6726219\times10^{-27}\,\mathrm{kg}$ and $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$.
   Special relativity
10. Q180 · Original practice · 6 marks
    An accelerator measures the following momentum magnitudes for the same particle. Use $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$.

    $v/c$	0.600	0.800	0.900
    $p$ ($10^{-19}\,\mathrm{kg\,m\,s^{-1}}$)	4.50	8.00	12.4

    Special relativity
11. Q181 · Original practice · 7 marks
    An electron and a positron initially at rest annihilate into two photons travelling in opposite directions with equal energies. Use $m_e=9.1093835\times10^{-31}\,\mathrm{kg}$, $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$, $h=6.626\times10^{-34}\,\mathrm{J\,s}$ and $1\,\mathrm{eV}=1.60\times10^{-19}\,\mathrm J$.
    Special relativity
12. Q182 · Original practice · 6 marks
    The graph shows two black-body spectra, each normalised separately so its own peak equals one. Their peak wavelengths are $966\,\mathrm{nm}$ for A and $483\,\mathrm{nm}$ for B. Use $b=2.898\times10^{-3}\,\mathrm{m\,K}$.
    Quantum theory
13. Q183 · Original practice · 6 marks
    The graph shows maximum photoelectron kinetic energy for metals M and N. Line M passes through $(6.00\times10^{14}\,\mathrm{Hz},1.3252\times10^{-19}\,\mathrm J)$ and $(9.00\times10^{14}\,\mathrm{Hz},3.3130\times10^{-19}\,\mathrm J)$. The frequency intercept of N is $6.00\times10^{14}\,\mathrm{Hz}$. Assume straight-line fits.
    Quantum theory
14. Q184 · Original practice · 7 marks
    A clean metal has work function $2.60\times10^{-19}\,\mathrm J$. It is illuminated at frequency $5.50\times10^{14}\,\mathrm{Hz}$. Use $h=6.626\times10^{-34}\,\mathrm{J\,s}$, $m_e=9.1093835\times10^{-31}\,\mathrm{kg}$ and $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$. Assume one-photon emission.
    Quantum theory
15. Q185 · Original practice · 7 marks
    An idealised atom has bound energy levels $-8.00$, $-3.00$ and $-1.00\,\mathrm{eV}$, with ionisation at $0\,\mathrm{eV}$. Its electron initially occupies the ground level. Incident photons have energies $4.00$, $5.00$, $7.00$ or $8.50\,\mathrm{eV}$. Ignore recoil and multi-photon processes. Use $h=6.626\times10^{-34}\,\mathrm{J\,s}$,…
    Quantum theory
16. Q186 · Original practice · 7 marks
    A hydrogen atom emits a photon as its electron falls from $n_i=5$ to $n_f=2$. Use $R=1.097\times10^7\,\mathrm{m^{-1}}$. A second hydrogen photon has wavelength $1.282\times10^{-6}\,\mathrm m$ and also begins from $n_i=5$.
    Quantum theory
17. Q187 · Original practice · 7 marks
    In the Bohr standing-wave model, an electron occupies an $n=3$ orbit of radius $4.76\times10^{-10}\,\mathrm m$. Use $h=6.626\times10^{-34}\,\mathrm{J\,s}$ and $m_e=9.1093835\times10^{-31}\,\mathrm{kg}$. Treat the electron momentum as nonrelativistic.
    Quantum theory
18. Q188 · Original practice · 7 marks
    Two observations are made: (1) monochromatic light passing through two narrow slits forms alternating bright and dark bands; (2) a metal shows a threshold frequency for immediate photoelectron emission, and no emission below threshold in the one-photon regime even at higher intensity.
    Quantum theory
19. Q189 · Original practice · 6 marks
    Particle X has quark content $uds$. Particle Y has quark content $d\bar s$. The quark charges are $Q_u=+2e/3$ and $Q_d=Q_s=-e/3$. Antiquarks have opposite charge and baryon number to their corresponding quarks.
    The Standard Model
20. Q190 · Original practice · 6 marks
    The interaction diagram shows a down quark in a neutron changing to an up quark. The emitted boson produces an electron and an unidentified particle X. A neutron is $udd$ and a proton is $uud$. Leptons have lepton number $+1$ and antileptons have $-1$.
    The Standard Model
21. Q191 · Original practice · 6 marks
    The particle interaction diagram shows two electrons scattering by exchange of a wavy line. Time increases upward. Incoming and outgoing external particles are all electrons.
    The Standard Model
22. Q192 · Original practice · 6 marks
    A proton and an antiproton collide. Consider only conservation of total electric charge, baryon number and lepton number when assessing these candidate final states: A: $n+\bar n$; B: $n+n$; C: $e^-+e^+$; D: $e^-+\bar\nu_e$. Neutrons are neutral baryons; neutrinos are neutral leptons. Antiparticle quantum numbers have opposite signs.
    The Standard Model
23. Q193 · Original practice · 7 marks
    Consider the Standard Model gauge bosons and the forces experienced by quarks and leptons. Gravity is outside this comparison.
    The Standard Model
24. Q194 · Original practice · 6 marks
    A $1.50\,\mathrm{MeV}$ photon produces an electron–positron pair in the field of a heavy nucleus. Use $m_e=9.1093835\times10^{-31}\,\mathrm{kg}$, $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$ and $1\,\mathrm{eV}=1.60\times10^{-19}\,\mathrm J$. The nucleus remains the same species and takes a small recoil energy.
    The Standard Model