BSc Sem VI 2014 2015 2015 Math 2 Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 (a) Attempt any one
   • (i) Obtain the Lorentz transformation equations for space time coordinates of 10 an event. State clearly where the postulates of the special theory of relativity have been used in the derivation
   • (ii) State the postulates of the special theory of relativity. Write the Lorentz 10 transformation equations for space - time coordinates of at: event (derivation not required). Hence derive the formulae for time dilation and length
   • (b) Attempt any one
   • (i) Assuming the Lorentz transformation equations for space time coordinates 5 of an event, derive the equation for the component of acceleration parallel to the of relative motion
   • (ii) Give the wavelength shift, if any, in the Doppler effect for the sodiumD, 5 line (5890 A) emitted from a source moving in a circle with constant speed measured by an observer fixed at the center of the circle
2. Q2 (a) Attempt any one
   • (i) Considering the Law of Conservation of momentum to be true in all inertial 10 frames, derive tite relation between the moving mass and rest mass,
   • (ii) Derive the relativistic kinetic energy equation 10 K= 1 | . Hence show that it reduces to the Newtonian expression for kinetic energy in the non relativistic limit
   • (b) Attemprany one What is the relativistic mass & momentum of a photon of frequency Vv? 5 Show that rest mass of a photon is zero The momentum of an electron observed in a magnetic deflectionexperiment 5 18 ; where m, is the rest mass of the electron and is the velocity Find the velocity of the electron @ Attempt any one. for field intensity E Derive the transformation two identical electric point charges 10 Gi) frame of reference S. Discuss the significance of the result
   • (b) Attempt any one. invari derLorentz 5 transformations of current density J & vo Gi) Show that a current carrying wire at rest in an inertial frame frame moving with uniform velocity with respect to S
3. Q4 (a) Attempt any one
   • (ii) Describe the large scale structure of the universe. 10
   • (b) Attempt any one
   • (i) Write a short note on X-ray astronomy. 5
   • (ii) Explain in brief the Twin-Paradox. 5
4. Q5 (a) Attempt any onc
   • (i) the proper time interval between the occurrence oftwoeventsifin 4 some inertial frame they are :- (p) Separated by and occur 5 seconds apart: (q) Separated by 7.5 10*m and occur 2.5 seconds apart, Separated by 5 x and occur 1.5 seconds apart ?
   • (ii) Assuming the Lorentz equations, show thatiftwoeventsare 4 simultaneous in one inertial frame, they may not be in another
   • (i) The density of goid is 19.3 4 What is its when it is moving with relative velocity ? the velocity of a body when its total energy isthreetimesitsrestenergy. 4
   • (c) Attempt any E - B is invariant under Lorentz transformations. 4 He purely electric in inertial frame S, describe it in another inertial 4
   • (d) any one
   • (ii) A star is approaching the 3 shift for the wavelength 5000

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