DP Physics Questionbank

• Syllabus

Option A: Relativity

Sub sections and their related questions

Option A: Relativity (Core topics)

• 15M.3.HL.TZ1.14a: An observer at rest relative to Earth observes two spaceships. Each spaceship is moving with a...
• 15M.3.HL.TZ1.14b: The observer on Earth in (a) watches one spaceship as it travels to a distant star at a speed of...
• 15M.3.SL.TZ1.11a: An observer at rest relative to Earth observes two spaceships. Each spaceship is moving with a...
• 15M.3.SL.TZ1.11b: The observer on Earth in (a) watches one spaceship as it travels to a distant star at a speed of...
• 15M.3.SL.TZ2.11a: Determine the time, in years, that it takes the spacecraft to reach the planet according to...
• 15M.3.SL.TZ2.11b: The spacecraft passes a space station that is at rest relative to the Earth. The proper length of...
• 15M.3.SL.TZ2.11c: F and B are two flashing lights located at the ends of the space station, as shown. As the...
• 15N.3.HL.TZ0.12a: State what is meant by an inertial frame of reference.
• 15N.3.HL.TZ0.12b.i: A light on the base station flashes regularly. According to Suzanne, the light flashes every 3...
• 15N.3.HL.TZ0.12b.ii: While moving away from the base station, Suzanne observes another spacecraft travelling towards...
• 15N.3.HL.TZ0.12c.i: Suzanne’s spacecraft is on a journey to a star. According to Juan, the distance from the base...
• 15N.3.HL.TZ0.12c.ii: Suzanne then returns to the base station at the same speed. The total time since leaving the base...
• 14M.3.SL.TZ1.8a: State what is meant by an inertial frame of reference.
• 14M.3.SL.TZ1.8b: A spaceship travels from space station Alpha to space station Zebra at a constant speed of 0.90c...
• 14M.3.SL.TZ1.8c: Explain which of the time measurements in (b)(i) and (b)(ii) is a proper time interval.
• 14M.3.SL.TZ1.8d: The spaceship arrives at Zebra and enters an airlock at constant speed. O is an observer at rest...
• 15N.3.SL.TZ0.12b.ii: While moving away from the base station, Suzanne observes another spacecraft travelling towards...
• 15N.3.SL.TZ0.12b.iii: Using the postulates of special relativity, state and explain why Galilean transformations cannot...
• 15N.3.SL.TZ0.12b.iv: Using relativistic kinematics, the relative speeds of the two spacecraft is shown to be 0.976c....
• 15N.3.SL.TZ0.12c: Suzanne’s spacecraft is on a journey to a star. According to Juan, the distance from the base...
• 14N.3.HL.TZ0.18a: Deduce that few muons would be expected to arrive at the surface of the Earth if non-relativistic...
• 14N.3.HL.TZ0.18b.i: Calculate the average decay time of a muon as observed by an observer on the surface of the Earth.
• 14N.3.HL.TZ0.18b.ii: Explain, with a calculation, why many muons reach the surface of the Earth before they have decayed.
• 14N.3.HL.TZ0.19a: Calculate the speed of the positron as measured in the frame of reference of the electron.
• 14N.3.SL.TZ0.11a: State and explain the order of arrival of X and Y at the mirrors according to Jaime.
• 14N.3.SL.TZ0.11b: Outline whether the return of X and Y to Daniela are simultaneous according to Jaime.
• 14N.3.SL.TZ0.12a: One of the postulates of special relativity refers to the speed of light. State the other...
• 14M.3.SL.TZ2.10a: State the reason why the time interval between event 1 and event 2 is a proper time interval as...
• 14M.3.SL.TZ2.10b: (i)     Calculate the time interval between event 1 and event 2 according to Peter. (ii)   ...
• 14M.3.SL.TZ2.10c: (i)     Calculate, according to Judy, the distance separating the Earth and planet P. (ii)   ...
• 13M.3.SL.TZ1.10a: Describe what is meant by a frame of reference.
• 13M.3.SL.TZ1.10b: At a later time the police spacecraft is alongside Speedy’s spacecraft. The police spacecraft is...
• 13M.3.SL.TZ1.10c: The police spacecraft is travelling at a constant speed of 0.5c relative to Speedy’s frame of...
• 13M.3.HL.TZ1.14b: Officer Sylvester switches on the blue flashing lamps on his police spacecraft. (i) Calculate,...
• 13M.3.HL.TZ2.16a: Show that, if the muons move at non-relativistic speed, the number of muons detected at sea level...
• 13M.3.HL.TZ2.16b: The muons in (a) move toward the surface of Earth with a relativistic speed of 0.968c. (i)...
• 12M.3.SL.TZ1.11a: State and explain whether the pendulum period is a proper time interval for observer T, observer...
• 12M.3.SL.TZ1.11b: Observer T measures the period of oscillations of the pendulum to be 0.850s. Calculate the period...
• 12M.3.SL.TZ1.11c: Observer T is standing in the middle of a train watched by observer G at the side of the track....
• 12M.3.HL.TZ1.11e: Observer G sees a second train moving towards the first train (i.e. towards the left) at a speed...
• 12M.3.HL.TZ1.12a: In an experiment at CERN in 1964, a neutral pion moving at a speed of 0.99975c with respect to...
• 11M.3.SL.TZ2.10a: Carrie measures her spaceship to have a length of 100m. Peter measures Carrie’s spaceship to have...
• 11M.3.SL.TZ2.10b: According to Carrie, it takes the star ten years to reach her. Using your answer to (a)(ii),...
• 11M.3.SL.TZ2.10c: According to Peter, as Carrie passes the star she sends a radio signal. Determine the time, as...
• 11M.3.HL.TZ2.10d: Carrie and Louise, two observers in a spaceship, view a light source placed close to Carrie. When...
• 11M.3.HL.TZ2.17a: Describe what is meant by spacetime.
• 11M.3.HL.TZ2.17b: State the shape of the path in spacetime of a body (i) moving at constant velocity. (ii)...
• 11N.3.SL.TZ0.9a: One of the two postulates of special relativity may be stated as: “The laws of physics are the...
• 11N.3.SL.TZ0.9b: In a thought experiment to illustrate the concept of simultaneity, Vladimir is standing on the...
• 11N.3.SL.TZ0.9c: The speed v of the carriage is 0.70c. Vladimir measures the length of the table at which Natasha...
• 11N.3.HL.TZ0.12e: Evidence for time dilation comes from the decay of muons. A pulse of muons produced by cosmic...
• 11N.3.HL.TZ0.12f: Suggest how your answers to (e)(i) and (e)(ii) provide evidence that supports the theory of...
• 12M.3.SL.TZ2.10a: State the postulate of special relativity that is related to the speed of light.
• 12M.3.SL.TZ2.10b: A rocket moving at a relativistic speed passes an observer who is at rest on the...
• 12N.3.SL.TZ0.12a: In the context of the theory of relativity, state what is meant by an event.
• 12N.3.SL.TZ0.12b: (i) Calculate the time interval t between event 1 and event 2 according to an observer in the...
• 12N.3.SL.TZ0.12c: Relative to an observer on the ground, (i) calculate the distance between S and D. (ii) state...
• 12N.3.HL.TZ0.16a: (i) Define the rest mass of a particle. (ii) The rest mass of a particle is said to be an...
• 12M.3.HL.TZ2.14a: Calculate the time it takes the pulse to travel from S to D, according to (i) an observer in the...
• 12M.3.HL.TZ2.14b: Calculate the distance between the source S and the detector D according to observer Q.
• 12M.3.HL.TZ2.14c: A particular nucleus in the pulse decays by emitting an electron in the same direction as that of...
• 12M.3.HL.TZ2.14d: The laboratory observer and observer Q agree that by the time the pulse arrives at D, half of the...
• 13N.3.HL.TZ0.12a: Two space stations X and Y are at rest relative to each other. The separation of X and Y as...
• 13N.3.HL.TZ0.12b: A radio signal is sent to both space stations in (a) from a point midway between them. On receipt...
• 13N.3.HL.TZ0.12d: Muons are produced in the upper atmosphere of Earth and travel towards the surface of Earth where...
• 13N.3.HL.TZ0.14a: Describe what is meant by spacetime.
• 13N.3.SL.TZ0.9a: Two space stations X and Y are at rest relative to each other. The separation of X and Y as...
• 13N.3.SL.TZ0.9b: A radio signal is sent to both space stations in (a) from a point midway between them. On receipt...
• 11M.3.SL.TZ1.11a: Define proper length.
• 11M.3.SL.TZ1.11b: A spaceship is travelling to the right at speed 0.75 c, through a tunnel which is open at both...
• 11M.3.SL.TZ1.11c: Two sources of light are located at each end of the tunnel. The diagram below shows...
• 11M.3.HL.TZ1.17a: Calculate the velocity of rocket 2 relative to the Earth, using the (i) Galilean transformation...
• 11M.3.HL.TZ1.17b: Comment on your answers in (a).
• 10N.3.HL.TZ0.H1g: The questions (e) and (f ) introduce the concepts of time dilation and length contraction....
• 10N.3.SL.TZ0.D1a: On the diagram, sketch the path of the light pulse between \({{\text{M}}_{\text{1}}}\) and...
• 10N.3.SL.TZ0.D1b: (i)     State, according to Jill, the distance moved by the spaceship in time \(\Delta t\). (ii)...
• 10N.3.SL.TZ0.D1c: State, according to special relativity, the length of the path of the light between...
• 10N.3.SL.TZ0.D1d: The time for the pulse to travel from \({{\text{M}}_{\text{2}}}\) to \({{\text{M}}_{\text{1}}}\)...
• 10N.3.SL.TZ0.D1e: According to a clock at rest with respect to Jill, a clock in the spaceship runs slow by a factor...
• 16M.3.SL.TZ0.3a: State what is meant by inertial in this context.
• 16M.3.SL.TZ0.3b: An observer is travelling at velocity v towards a light source. Determine the value the observer...
• 16M.3.SL.TZ0.4: Two protons are moving with the same velocity in a particle accelerator.Observer X is at rest...
• 16M.3.SL.TZ0.5a: For the reference frame of the electron, calculate the distance travelled by the detector.
• 16M.3.SL.TZ0.5b: For the reference frame of the laboratory, calculate the time taken for the electron to reach the...
• 16M.3.SL.TZ0.5c: For the reference frame of the electron, calculate the time between its emission at the nucleus...
• 16M.3.SL.TZ0.5d: Outline why the answer to (c) represents a proper time interval.
• 16M.3.SL.TZ0.6a: For the reference frame of the Earth observer, calculate the speed of rocket A in terms of the...
• 16M.3.SL.TZ0.6b: Using the graph opposite, deduce the order in which (i) the beacons flash in the reference frame...
• 16M.3.HL.TZ0.5b: The electron is detected at a distance of 0.800 m from the emitting nucleus as measured in the...
• 16M.3.HL.TZ0.6a: For the reference frame of the Earth observer, calculate the speed of rocket A in terms of the...
• 16M.3.HL.TZ0.6b: One rocket passes the other at event E. For the reference frame of the Earth observer,...
• 16M.3.HL.TZ0.6c: Three flashing light beacons, X, Y and Z, are used to guide another rocket C. The flash events...
• 16N.3.SL.TZ0.4a: Define frame of reference.
• 16N.3.SL.TZ0.4b: In the reference frame of the laboratory the force on X is magnetic. (i) State the nature of the...
• 16N.3.SL.TZ0.5a: Define proper length.
• 16N.3.SL.TZ0.5b: A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in...
• 16N.3.SL.TZ0.5c: In the pion reference frame, the Earth moves a distance X before the pion decays. In the Earth...
• 16N.3.SL.TZ0.6a: Calculate the angle between the worldline of S and the worldline of the Earth.
• 16N.3.SL.TZ0.6b: Draw, on the diagram, the x′-axis for the reference frame of S.
• 16N.3.SL.TZ0.6c: An event Z is shown on the diagram. Label the co-ordinates of this event in the reference frame...
• 16N.3.SL.TZ0.7a: Calculate the time taken for the journey in the reference frame of twin A as measured on Earth.
• 16N.3.SL.TZ0.7b: Determine the time taken for the journey in the reference frame of twin B.
• 16N.3.SL.TZ0.7c: Draw, for the reference frame of twin A, a spacetime diagram that represents the worldlines for...
• 16N.3.SL.TZ0.7d: Suggest how the twin paradox arises and how it is resolved.
• 17M.3.SL.TZ1.3a: State what is meant by a reference frame.
• 17M.3.SL.TZ1.3b.i: State and explain whether the force experienced by P is magnetic, electric or both, in reference...
• 17M.3.SL.TZ1.3b.ii: State and explain whether the force experienced by P is magnetic, electric or both, in the rest...
• 17M.3.SL.TZ1.4a: State which of the two time intervals is a proper time.
• 17M.3.SL.TZ1.4b: Calculate the speed v of the train for the ratio...
• 17M.3.SL.TZ1.4c: Later the train is travelling at a speed of 0.60c. Observer P measures the length of the train to...
• 17M.3.SL.TZ1.4d.i: Draw the time \(ct'\) and space \(x'\) axes for observer P’s reference frame on the spacetime...
• 17M.3.SL.TZ1.4d.ii: Deduce, using the spacetime diagram, which light was turned on first according to observer P.
• 17M.3.SL.TZ1.4d.iii: Apply a Lorentz transformation to show that the time difference between events B and F according...
• 17M.3.SL.TZ1.4d.iv: Demonstrate that the spacetime interval between events B and F is invariant.
• 17M.3.SL.TZ1.4e: A second train is moving at a velocity of –0.70c with respect to the ground. Calculate the...
• 17M.3.SL.TZ2.3a: State one prediction of Maxwell’s theory of electromagnetism that is consistent with special...
• 17M.3.SL.TZ2.3b: A current is established in a long straight wire that is at rest in a laboratory. A proton is...
• 17M.3.SL.TZ2.4: Muons are unstable particles with a proper lifetime of 2.2 μs. Muons are produced 2.0 km above...
• 17M.3.SL.TZ2.5a.i: Calculate the length of the rocket according to X.
• 17M.3.SL.TZ2.5a.ii: A space shuttle is released from the rocket. The shuttle moves with speed 0.20c to the right...
• 17M.3.SL.TZ2.5b.i: the time interval between the lamps turning on.
• 17M.3.SL.TZ2.5b.ii: which lamp turns on first.
• 17M.3.SL.TZ2.5c.i: On the diagram label the coordinates x and ct.
• 17M.3.SL.TZ2.5c.ii: State and explain whether the ct coordinate in (c)(i) is less than, equal to or greater than 1.0 m.
• 17M.3.SL.TZ2.5c.iii: Calculate the value of c 2t 2 – x 2.
• 17N.3.SL.TZ0.4: Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates...
• 17N.3.SL.TZ0.5a: Define frame of reference.
• 17N.3.SL.TZ0.5b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
• 17N.3.SL.TZ0.5c: Identify the terms in the formula. u′ = \(\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}\)  
• 17N.3.SL.TZ0.5d: Determine, according to an observer in A, the velocity of B.
• 17N.3.SL.TZ0.5e.i: Determine, according to an observer in A, the time taken for B to meet A.
• 17N.3.SL.TZ0.5e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an observer...
• 17N.3.SL.TZ0.6b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
• 17N.3.SL.TZ0.6c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
• 17N.3.SL.TZ0.6d: For an observer on the train, it is the tunnel that is moving and therefore will appear length...
• 18M.3.SL.TZ1.3a: State whether the field around the wire according to observer X is electric, magnetic or a...
• 18M.3.SL.TZ1.3b.i: Discuss the change in d according to observer Y.
• 18M.3.SL.TZ1.3b.ii: Deduce whether the overall field around the wire is electric, magnetic or a combination of both...
• 18M.3.SL.TZ1.4a.i: Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
• 18M.3.SL.TZ1.4a.ii: Deduce why only a small fraction of the total number of muons created is expected to be detected...
• 18M.3.SL.TZ1.4b.i: Calculate, according to the theory of special relativity, the time taken for a muon to reach the...
• 18M.3.SL.TZ1.4b.ii: Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory...
• 18M.3.SL.TZ1.5a: Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
• 18M.3.SL.TZ1.5b: Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth...
• 18M.3.SL.TZ1.5c: Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous...
• 18M.3.SL.TZ1.5d: Calculate the velocity of rocket B relative to rocket A.
• 18M.3.SL.TZ2.3a.i: Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean...
• 18M.3.SL.TZ2.3a.ii: Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz...
• 18M.3.SL.TZ2.3b: Outline, with reference to special relativity, which of your calculations in (a) is more likely...
• 18M.3.SL.TZ2.4a: Calculate the velocity of the spaceship relative to the Earth.
• 18M.3.SL.TZ2.4b: The spaceship passes the space station 90 minutes later as measured by the spaceship clock....
• 18M.3.SL.TZ2.4c: As the spaceship passes the space station, the space station sends a radio signal back to the...
• 18M.3.SL.TZ2.4d.i: Construct event A and event B on the spacetime diagram.
• 18M.3.SL.TZ2.4d.ii: Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
• 18M.3.SL.TZ2.5a: Explain what is meant by the statement that the spacetime interval is an invariant quantity.
• 18M.3.SL.TZ2.5b.i: calculate the spacetime interval.
• 18M.3.SL.TZ2.5b.ii: determine the time between them according to observer B.
• 18M.3.SL.TZ2.5c: Outline why the observed times are different for A and B.

Option A: Relativity (Additional higher level option topics)

• 15M.3.HL.TZ1.15a: Calculate the speed of an electron when its total energy is equal to five times its rest mass...
• 15M.3.HL.TZ1.15b: The electron is accelerated from rest through a potential difference V. The graph shows how the...
• 15M.3.HL.TZ1.16a: Calculate the Schwarzschild radius for an astronomical object of mass 5.0 ×1030 kg.
• 15M.3.HL.TZ1.16b: A spaceship is travelling towards the object in (a). The spaceship moves in a straight line such...
• 15M.3.HL.TZ1.16c: An observer, when viewing a distant galaxy, sees two images of the galaxy separated by a small...
• 15M.3.HL.TZ2.16a: total energy.
• 15M.3.HL.TZ2.16b: momentum.
• 15M.3.HL.TZ2.16c: speed.
• 15M.3.HL.TZ2.17a: Newton’s universal law of gravitation.
• 15M.3.HL.TZ2.17b: Einstein’s theory of general relativity.
• 15M.3.HL.TZ2.18a: A ray of light is moving at right angles to the direction of the rocket according to the same...
• 15N.3.HL.TZ0.13a.i: Using the grid, sketch a graph showing how the energy of the kaon increases with speed.
• 15N.3.HL.TZ0.13a.ii: The kaon is accelerated from rest through a potential difference so that its energy becomes three...
• 15N.3.HL.TZ0.13b: The neutral kaon is unstable and one of its possible modes of decay...
• 15N.3.HL.TZ0.15a.i: Show that the gravitational field strength at the surface of the planet is about...
• 15N.3.HL.TZ0.15a.ii: Discuss the shift in frequency of the laser beam.
• 15N.3.HL.TZ0.15b: The spacecraft leaves the planet with an acceleration of \({\text{5.7 m}}\,{{\text{s}}^{ - 2}}\)....
• 14M.3.HL.TZ1.16: This question is about relativistic dynamics. A proton is accelerated from rest through a...
• 14M.3.HL.TZ1.18a: State the principle of equivalence.
• 14M.3.HL.TZ1.18b: An observer in a spaceship moving at constant speed measures the frequency f0 of light emitted by...
• 14M.3.HL.TZ1.19: This question is about evidence that supports general relativity. The astronomical photograph...
• 14N.3.HL.TZ0.19b.i: Calculate the total energy in the reaction.
• 14N.3.HL.TZ0.19b.ii: Outline why two photons must be released in this collision.
• 14N.3.HL.TZ0.19b.iii: Determine the frequency of one of the photons.
• 14N.3.HL.TZ0.20a: Explain why the light reaching the space station will be red-shifted.
• 14N.3.HL.TZ0.20b: The time between the pulses as measured by the observer on the distant space station is found to...
• 14M.3.HL.TZ2.16a: (i)     Show that the initial momentum of the pion is...
• 14M.3.HL.TZ2.16b: The pion \(({\pi ^ + })\) emits a muon in the same direction as the velocity of the pion. The...
• 14M.3.HL.TZ2.17b: (i)     \({f_{\text{C}}}\) (ii)     \({f_{\text{P}}}\)
• 14M.3.HL.TZ2.17c: Newton explained the motion of a planet around the Sun in terms of a force of gravitation between...
• 13M.3.HL.TZ1.15a: A proton is accelerated from rest by a potential difference V and reaches a speed of 2.5×108 m...
• 13M.3.HL.TZ1.16a: Deduce the change in the frequency of the gamma rays, as measured by the observer, when the...
• 13M.3.HL.TZ1.16b: Outline, with reference to the principle of equivalence, how the situation in (a) relates to the...
• 13M.3.HL.TZ1.17a: Explain, with reference to the warping of spacetime, the gravitational attraction between Earth...
• 13M.3.HL.TZ1.19a: Sirius B has a mass of 2.0×1030 kg. Calculate the minimum density required for Sirius B to...
• 13M.3.HL.TZ2.17a: Calculate the value of V.
• 13M.3.HL.TZ2.18b: Calculate the speed of the proton after acceleration.
• 13M.3.HL.TZ2.19a: State the equivalence principle.
• 13M.3.HL.TZ2.19b: A helium filled balloon is floating in air inside a spacecraft in outer space. The...
• 13M.3.HL.TZ2.19c: In an experiment, to verify the bending of light as it passes close to the Sun, the position of a...
• 12M.3.HL.TZ1.12b: In another experiment, a neutral pion moving at 0.80c relative to a laboratory decayed into two...
• 12M.3.HL.TZ1.13a: State the principle of equivalence.
• 12M.3.HL.TZ1.13b: The gravitational field strength near the surface of a neutron star is 1.2 ×1013Nkg–1. A light...
• 12M.3.HL.TZ1.13c: General relativity predicts the existence of black holes. (i) State what is meant by a black...
• 11M.3.HL.TZ2.15a: Calculate the potential difference through which a proton, starting from rest, must be...
• 11M.3.HL.TZ2.15b: Calculate the momentum of the proton after acceleration.
• 11M.3.HL.TZ2.17c: Explain how spacetime is used to describe the gravitational attraction between Earth and a...
• 11N.3.HL.TZ0.13a: A proton is accelerated from rest through a potential difference V. The proton reaches a speed of...
• 11N.3.HL.TZ0.13b: Calculate, after acceleration for the proton in (a), its (i) mass. (ii) momentum.
• 11N.3.HL.TZ0.14a: Outline why, if the spaceship now accelerates, Kim will measure the light from L1 to be...
• 11N.3.HL.TZ0.14b: Suggest, with reference to Einstein’s principle of equivalence, how your answer to (a) leads to...
• 12N.3.HL.TZ0.16b: In a thought experiment, two particles X and Y, each of rest mass 380 MeVc–2, are approaching...
• 12N.3.HL.TZ0.17a: State the principle of equivalence.
• 12N.3.HL.TZ0.17b: A gamma-ray photon is emitted from the base of a tower towards the top of the tower. (i)...
• 12N.3.HL.TZ0.18a: Define the Schwarzschild radius of a black hole.
• 12N.3.HL.TZ0.18b: Explain, using the concept of spacetime, why the path of the light ray is straight at distances...
• 12M.3.HL.TZ2.15a: The graph shows the variation with the fraction \(\frac{v}{c}\), of the kinetic energy EK of a...
• 12M.3.HL.TZ2.15b: Determine, using data from the graph, the potential difference required to accelerate...
• 12M.3.HL.TZ2.16a: Show that the speed v of a particle of total energy E and momentum p is given by the following...
• 12M.3.HL.TZ2.16b: Determine, using the answer in (a), the speed of a particle whose rest mass is zero.
• 12M.3.HL.TZ2.17a: State the equivalence principle.
• 12M.3.HL.TZ2.17b: The diagram shows two identical boxes in two different states of motion. In diagram 1 the box...
• 12M.3.HL.TZ2.17c: Radio signals, sent at the same time from Earth, reflect off two satellites X and Y as shown. The...
• 13N.3.HL.TZ0.13a: A proton is accelerated from rest through a potential difference V. After acceleration the mass...
• 13N.3.HL.TZ0.13b: For the proton in (a) calculate, after acceleration, its (i) speed. (ii) momentum.
• 13N.3.HL.TZ0.14b: Outline how the concept of spacetime accounts for the (i) orbiting of Earth about the Sun. (ii)...
• 11M.3.HL.TZ1.17c: The rest mass of rocket 1 is 1.0×103kg. Determine the relativistic kinetic energy of rocket 1, as...
• 11M.3.HL.TZ1.19a: (i) State how the frequency as measured by observer B compares with the frequency as measured by...
• 11M.3.HL.TZ1.19b: The lasers are now placed on a spaceship, which is accelerating upwards at a constant rate of...
• 10N.3.HL.TZ0.H2a: Calculate, immediately after the decay, the magnitude of the momentum of the electron.
• 10N.3.HL.TZ0.H2b: Calculate the value \(V\) of the potential difference through which an electron at rest must be...
• 10N.3.HL.TZ0.H3a: State and explain whether, from the path followed by the ball, Bob can deduce that the spaceship...
• 10N.3.HL.TZ0.H3b: Outline how the concept of spacetime can be used to explain the (i)     trajectory of the ball...
• 10N.3.HL.TZ0.H3c: Calculate the radius that Earth would have to have in order for it to behave as a black hole. The...
• 16M.3.HL.TZ0.5b: The electron is detected at a distance of 0.800 m from the emitting nucleus as measured in the...
• 16M.3.HL.TZ0.5a: Show that the speed of the electron is about 0.98c.
• 16M.3.HL.TZ0.7b: An observer views a distant spacecraft that is 23.0 km from the centre of a black hole. The...
• 16N.3.HL.TZ0.8a: Explain, in terms of a conservation law, why two photons need to be created.
• 16N.3.HL.TZ0.8b: Determine the speed of the incoming electron.
• 16N.3.HL.TZ0.8c: Calculate the energy and the momentum for each photon after the collision.
• 16N.3.HL.TZ0.9a: The gravitational field strength at 20 Mm above the surface of the Earth is about 0.6 N kg–1....
• 16N.3.HL.TZ0.9b: Suggest, whether your answer to (a) underestimates or overestimates the correction required to...
• 17M.3.HL.TZ1.5a: Calculate the potential difference V.
• 17M.3.HL.TZ1.5b: The proton collides with an antiproton moving with the same speed in the opposite direction. As a...
• 17M.3.HL.TZ1.6a: Calculate the expected shift in frequency between the emitted and the detected gamma rays.
• 17M.3.HL.TZ1.6b: Explain whether the detected frequency would be greater or less than the emitted frequency.
• 17M.3.HL.TZ2.6: A lambda \(\Lambda \)0 particle at rest decays into a proton p and a pion \({\pi ^ - }\)...
• 17M.3.HL.TZ2.7a.i: State what is meant by the event horizon of a black hole.
• 17M.3.HL.TZ2.7a.ii: Show that the surface area A of the sphere corresponding to the event horizon is given...
• 17M.3.HL.TZ2.7a.iii: Suggest why the surface area of the event horizon can never decrease.
• 17M.3.HL.TZ2.7b: The diagram shows a box that is falling freely in the gravitational field of a planet. A...
• 17N.3.HL.TZ0.7a: Determine the rest mass of the \({\Lambda ^0}\) particle.
• 17N.3.HL.TZ0.7b: Determine, using your answer to (a), the initial speed of the \({\Lambda ^0}\) particle.
• 17N.3.HL.TZ0.8a: Outline why the clock near the black hole runs slowly compared to a clock close to the distant...
• 17N.3.HL.TZ0.8b: Calculate the number of ticks detected in 10 ks by the distant observer.
• 18M.3.HL.TZ1.6a.ii: show that the energy of the pion is about 140 MeV.
• 18M.3.HL.TZ1.6b: State the rest mass of the pion with an appropriate unit.
• 18M.3.HL.TZ1.7a: Calculate the shift in frequency observed by A in terms of Δf.
• 18M.3.HL.TZ1.7b: Calculate the gravitational field strength on the surface of planet X.                          ...
• 18M.3.HL.TZ1.7c: Observer A now sends a beam of light initially parallel to the surface of the planet. Explain...
• 18M.3.HL.TZ2.6a: Calculate the gamma (γ) factor for one of the protons.
• 18M.3.HL.TZ2.6b.i: Determine, in terms of MeV c–1, the momentum of the pion.
• 18M.3.HL.TZ2.6b.ii: The diagram shows the paths of the incident protons together with the proton and neutron created...
• 18M.3.HL.TZ2.7a.i: Outline what is meant by the event horizon of a black hole.
• 18M.3.HL.TZ2.7a.ii: Calculate the distance of the event horizon of the black hole from its centre.                  ...
• 18M.3.HL.TZ2.7b: Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of...