THIS PAPER CARRIES 30 MARKS
3rd March 2025.
Research Test Exam, to be submitted on Friday,7 March
2025.
“Please respect the deadline”
QUESTIONS ON RELATIVITY
1. (a) State the two postulates of the special theory of relativity. (2 marks)
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(b) What is meant by the following terms:
(i) Inertial frame of reference
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(ii) proper time
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(iii) proper length
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Total marks: (3 marks)
(b) Two identical spacecraft are moving in opposite directions, each with
a speed of 0.80c as measured by an observer at rest relative to the ground. The observer
on the ground measures the separation of the spacecraft as increasing at a rate of 1.60c.
(i) Explain how this observation is consistent with the theory of special relativity. (1
mark)
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(ii) Calculate the speed of one spacecraft relative to an observer in the other. (2 marks)
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About time dilation
2. Two spaceships, A and B, pass in space at relative velocity 0.7c. An observer
on A measures the time between swings of a pendulum he holds to be 2 s. What will the
period be to an observer in B? (2 marks)
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3. The half-life of the decay of some radioactive isotope is 30 s. The nucleus is
accelerated to a speed of 0.99c relative to some observer. What will the half-life be to that
observer? (2 marks)
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About proper length
4. Two spaceships, A and B, pass in space at relative velocity 0.7c. If an observer
In B measures the length of a metal rod he is holding to be 2 m, what is the length of the
rod as measured by an observer in A? (2 marks)
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5. A nucleus decays 2 x 10-8 s (measured in the nucleus' frame of reference) after
passing an observer standing on the Earth traveling at a speed of 0.99c.
(a) Calculate how far the nucleus traveled in the nucleus' frame of reference.
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(b) Calculate the time of flight as measured by the Earth observer.
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(c) Calculate the distance traveled as measured by the Earth observer.
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(d) Which observer measured the proper time?
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(e) Which observer measured the proper distance?
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( Total marks: 5)
About the addition of velocity
6. Two subatomic particles are collided head on in a particle accelerator. Each
particle has a velocity of 0.9c relative to the Earth. Calculate the velocity
of one of the particles, as measured in the frame of reference of the other
particle. (2 marks)
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7. An observer on Earth sees a meteorite traveling at 0.5c on collision course
with a spaceship traveling at 0.6c. What is the velocity of the meteorite as
measured by the spaceship? ( 2 marks)
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8. Explain the Muon experiment. ( 3 marks)
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9. Figure below is a space-time diagram for two frames of reference traveling at 0.5c
relative to each other. Use it to estimate the answers to the following questions.
(a)Estimate the position and time in S' of an event that takes place at a
position 4 light years from the origin at a time of 6.5 years from the time
when the clocks were started in S. Check your solution using the Lorentz
transformations and (2 marks)
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(b)Find the space-time interval for the event in each frame. (2 marks)
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THE END
