TUTORIAL SHEET: 1
(Module1: Special Theory of Relativity)
1. Describe the Michelson Morley experiment and discuss the importance of its negative result. 2. Calculate the fringe shift in Michelson-Morley experiment. Given that: [pic], [pic], [pic], and [pic]. 3. State the fundamental postulates of Einstein special theory of relativity and deduce from them the Lorentz Transformation Equations . 4. Explain relativistic length contraction and time dilation in special theory of relativity? What are proper length and proper time interval? 5. A rod has length 100 cm. When the rod is in a satellite moving with velocity 0.9 c relative to the laboratory, what is the length of the rod as measured by an observer (i) in the satellite, and (ii) in the laboratory?. 6. A clock keeps correct time. With what speed should it be moved relative to an observer so that it may appear to lose 4 minutes in 24 hours? 7. In the laboratory the ‘life time’ of a particle moving with speed 2.8x108m/s, is found to be 2.5x10-7 sec. Calculate the proper life time of the particle. 8. Derive relativistic law of addition of velocities and prove that the velocity of light is the same in all inertial frame irrespective of their relative speed. 9. Two particles come towards each other with speed 0.9c with respect to laboratory. Calculate their relative speeds. 10. Rockets A and B are observed from the earth to be traveling with velocities 0.8c and 0.7 c along the same line in the same direction. What is the velocity of B as seen by an observer on A? 11. Show that the relativistic invariance laws of conservation of momentum leads to the concept of variation of mass with speed and mass energy equivalence. 12. A proton of rest mass [pic] is moving with a velocity of 0.9c. Calculate its mass and momentum. TUTORIAL SHEET: 1
(Module1: Special Theory of Relativity)
13. The speed of an electron is doubled from 0.2 c to 0.4 c. By what ratio does its momentum increase? 14. A particle has kinetic energy 20 times its rest energy. Find the speed of the particle in terms of ‘c’. 15. Dynamite liberates about 5.4x106 J/Kg when it explodes. What fraction of its total energy is in this amount? 16. A stationary body explodes into two fragments each of mass 1.0 Kg that move apart at speeds of 0.6 c relative to the original body. Find the mass of the original body. 17. At what speed does the kinetic energy of a particle equals its rest energy? 18. What should be the speed of an electron so that its mass becomes equal to the mass of proton? Given: mass of electron=9.1x10-31Kg and mass of Proton =1.67x10-27Kg.
19. An electron is moving with a speed 0.9c. Calculate (i) its total energy and (ii) the ratio of Newtonian kinetic energy to relativistic energy. Given: [pic] and[pic]. 20. (i) Derive a relativistic expression for kinetic energy of a particle in terms of momentum. (ii) Show that the momentum of a particle of rest mass [pic] and kinetic energy [pic], is given by[pic]. 21. Find the momentum (in MeV/c) of an electron whose speed is 0.60 c. Verify that v/c = pc/E TUTORIAL SHEET: 2(a)
(Module2: Wave Mechanics)
1. What do you understand by the wave nature of matter? Obtain an expression of de Broglie wavelength for matter waves. 2. Calculate the de-Broglie wavelength of an electron and a photon each of energy 2eV. 3. Calculate the de-Broglie wavelength associated with a proton moving with a velocity equal to 1/20 of the velocity of light. 4. Show that the wavelength of a 150 g rubber ball moving with a velocity of [pic] is short enough to be determined. 5. Energy of a particle at absolute temperature T is of the order of [pic]. Calculate the wavelength of thermal neutrons at[pic]. Given: [pic], [pic] and [pic]. 6. Can a photon and an electron of the same momentum have the same wavelengths? Calculate their wavelengths if the two have the same energy. 7. Two particles A and B are in motion. If the wavelength associated with particle A is [pic],...
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