Tutorial-IV (Special Relativity: Doppler Effect, Relativistic Energy, Momentum & Related Problems) PDF

JUET Guna/B.Tech./Sem-I/2024 Engineering Physics-1 (PH101) Tutorial-IV (Special Relativity: Doppler Effect, Relativistic Energy, Momentum & Related Problems) Important: me = 9.1093 × 10−31 kg, mp = 1.6726 × 10−27 kg, mn =...

JUET Guna/B.Tech./Sem-I/2024 Engineering Physics-1 (PH101) Tutorial-IV (Special Relativity: Doppler Effect, Relativistic Energy, Momentum & Related Problems) Important: me = 9.1093 × 10−31 kg, mp = 1.6726 × 10−27 kg, mn = 1.6749 × 10−27 kg 1. A car is approaching a radar speed trap at 80 mi/hr. If the radar set works at a frequency of 20 × 109 Hz, what frequency shift is observed by the patrolman at the radar set? 2. A star is receding from the earth at a speed of 5 × 10−3 c. What is the wavelength shift for the sodium D2 line (5890 Å)? 3. Suppose that the Doppler shift in the sodium D2 line (5890 Å) is 100 Å when the light is observed from a distant star. Determine the star’s velocity of recession. 4. A man in a rocket ship moving with a speed of 0.6c away from a space platform shines a light of wavelength 5000 Å toward the platform. What is the frequency of the light as seen by an observer on the platform? Further, what is the frequency of the light as seen by a passenger in a second rocket ship that moves in the opposite direction with a speed of 0.8c relative to the space platform? 5. A body at rest spontaneously breaks up into two parts which move in opposite directions. The parts have rest masses of 3 kg and 5.33 kg and respective speeds of 0.8c and 0.6c. Find out the rest mass of the original body. 6. What is the speed of an electron that is accelerated through a potential difference of 105 V? 7. Calculate the momentum of an electron having 1 MeV kinetic energy. Further cal- culate the momentum of an electron having 1 MeV total energy. 8. Calculate the kinetic energy of a proton whose velocity is 0.8c. 9. Calculate the velocity of an electron whose kinetic energy is 2 MeV. 10. Calculate the momentum of an electron whose velocity is 0.8c. 11. Show that: E 2 = p2 c2 + m20 c4 12. Calculate the kinetic energy of a neutron whose momentum is 200 MeV/c. 13. What is the mass of a proton whose kinetic energy is 1 GeV? 14. The rest mass of a µ−meson is 207 me where me is the rest mass of an electron electron, and its average lifetime when at rest is 2 × 10−6 s. What is the mass of a µ−meson if its average lifetime in the laboratory is 7 × 10−6 s? 15. Compute the effective mass of a 5000 Å photon. 16. An electron is accelerated to an energy of 2 GeV by an electron synchrotron. What is the ratio of the electron’s mass to its rest mass? 17. An electron is accelerated from rest to a velocity of 0.5c. Calculate its change in energy. 18. At what fraction of the speed of light must a particle move so that its kinetic energy is double its rest energy? 19. An electron’s velocity is 5 × 107 ms−1. How much energy is needed to double the speed? 20. An electron moves in the laboratory with a speed of 0.6c. An observer moves with a velocity of 0.8c along the direction of motion of the electron. What is the energy of the electron as determined by the observer? 21. A particle has a total energy of 6 × 103 MeV and a momentum of 3 × 103 MeV/c. What is its rest mass? Further what is the energy of the particle in a frame where its momentum is 5 × 103 MeV/c? 22. A particle of rest mass m0 moving with a speed of 0.8c makes a completely inelastic collision with a particle of rest mass 3m0 that is initially at rest. What is the rest mass of the resulting single body? 23. Suppose that the relativistic mass of a particle is 5% larger than its rest mass. What is its velocity? 24. What is the ratio of the relativistic mass to the rest mass for (a) an electron (b) a proton proton, when it accelerates from rest through a potential difference of 15 × 106 V? 25. An electron has kinetic energy equal to its rest energy. Show that the energy√of a photon which has the same momentum as this electron is given by EP h = 3E0 where E0 = m0 c2. Page 2