BSc Physics SEM VI 2018 19 Apr 2018-19 PHYSICS SPECIAL THEORY OF RELATIVITY Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 Attempt any two
   • (i) What is Lorentz Fitzgerald contraction hypothesis? How does it explain 10 the negative result of Michelson-Morley experiment? Why was it
   • (ii) Write notes on the following: 10
   • (a) Relativity of simultaneity
   • (b) Inertial and non-inertial frame of reference
   • (iii) State the basic postulates of special theory of relativity. Obtain the Lorentz 10 Transformation equations of space and time stating clearly where and how the postulates are used
2. Q2 Attempt any two
   • (i) Assuming Lorentz transformation equation for velocity, derive Lorentz 10 transformation equation for acceleration (only x component)
   • (ii) relativistic equations for Doppler effect in light. Show that when the 10 velocity of the moving frame is much compared to the velocity of light the relativistic formula reduces to the classical one Two events occurring at different points are simultaneous in one frame of reference but are not simultaneous in another frame of reference which is in different state of motion
3. Q3 Attempt any two
   • (i) Derive Lorentz transformations equations for force components. 10
   • (i) Show that E* = and prove that where energy, p is momentum of a body with rest mass m,
   • (iii) Starting with equation of force, derive Einstein’s mass energy relation 10
4. Q4 Attempt any two
   • (1) Explain in detail the gravitational red shift, hence obtain the expression 10 for modified frequency of photons when it is emitted from the star and Paper Subject Code: 88647 Physics: Special Theory of Relativity
   • (i) Lorentz transformation for E and B and the space time co-ordinates 10 prove the invariance of the following Maxwell’s equation Curl E= Assume that div B= 0 is invariant the transformation equation for magnetic field B using Lorentz 10 transformation equation for force
5. Q5 Attempt any four. (5 marks each) 20 marks
   • (1) A ball of mass moving with a velocity of along the x axis of frame S approaches a second particle of mass moving at velocity of u2=-3m/s along this axis. After head —on collision, it is found that m2 has a velocity Uz=+3m/s along the x-axis. Calculate the expected velocity of m1, after the collision
   • (ii) Calculate the length and the orientation of a rod of length 5m in a frame of reference which is moving with velocity 0.6c in a direction making angle with the rod
   • (iii) Two electrons approach each other with the same velocity of 0.8c relative to an observer. Calculate their relative velocity
   • (iv) Write a note on twin paradox
   • (v) Calculate the velocity of an electron having total energy 5 MeV. Rest mass of electron =9.1 X Kg ,c=
   • (vi) Find the momentum of photon having energy 2 eV. c= (vil) Show that the scalar product of invariant under Lorentz transformations for Eand B
   • (viii) If asmall box has electric charge density as 1 C/m*when observed at rest, determine its charge density when the box starts moving at a speed of 0.8c with respect to the observer

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