BSc Physics SEM VI 2016 17 2016-17 Special Theory Of Relativity & Indtrn Cosmology Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q3 Draw right indicate full marks
2. Q5 Use of log usual meaning unless otherwise stated
3. Q1 a) Attempt any one: able and non-programmable calculator is allowed
   • i) Derive the
   • ii) State the postulates for aberration of light and Doppler's effect in relativity. space and time derive theory of relativity and using Lorentz transformation equations of formula for length contraction and time dilation i source of light speed 0.6c relative to Sodium D2 line and is moving along a circle with constant (05) i by the fixed at the centre of the circle. Find the wavelength of light as 10
   • ii) i Ow that the space-time x? + y? + 72. invariant under Lorentz transformation equations of (05) ).2 a) Attempt any one:
   • i) Applying the princi between conservation of linear momentum to the perfectly elastic collision (10) ical particles in inertial frame of reference, obtain an expression for relativistic
   • ii) Derive the i ) expressions for longitudinal and transverse mass with respect to the direction of motion (10) of two inertial frames
   • b) Attempt any one:
   • i) Derive relativistic relation between total energy E and momentum p 5
   • ii) The density of silver is 10.5gm/cm? when it is at rest relative to an observer. What is its density when it is moving with relative velocity 0.8c 3 a) Attempt any one: 5
   • i) Derive the transformations for electric field intensity E using Lorentz transformations equations 10
   • ii) Two equal charges +q separated by distance r lying in XY plane relative to the frame S and having same X coordinate are moving with same velocity along X axis relative to the frame S. Using Lorentz transformation of force find the resultant force exerted by the two charges on each other 10
   • b) Attempt any one:--- of 5
   • i) Show that the scalar product E.B is invariant under the
   • ii) If charge kept stationary In inertial frame s', Deter
   • B.in inertial frame, t velocity assume that S' is Moving with respect to s along axis with
4. Q4 a) Attempt any for
   • j) Discuss in brief optical, X ray and Radio Astronomy: tral
   • ii) Explain the phenomenon of gravitational red- shift of the modified frequency of the spectral line
   • b) Attempt any one:
   • i) Explain the Twin Paradox in brief. relativity
   • ii) With the help of Minkowski space time diagram explain
5. Q5 a) Attempt any to be 98 (
   • i) A spaceship is 100 m long on the ground. When it is in speed. Given = with 4 velo
   • ii) A vector is represented as + + 5K ina related toa stationary frame. What is the vector FeP
   • b) Attempt any each Vv
   • i) Two identical particles of rest mass Mo forming a new particle of rest collide head on. The particles stick after are conserved, mass Mo, which is at rest. Show that though rest mass is not conserved 2 mo): 1402 km and the earth receives energy at
   • ii) The distance between the sun and the earth is 1-5 * of the the rate of 1.34 x Find the annual toss of the
   • C) Attempt any rmations for current and c
   • i) Show that is invariant under Lorentz transfo
   • ii) If a small box has electric charge density a5 when observe rmine its density when the box starts moving at speed of with respect to observer
   • d) Attempt any
   • i) Give brief account of ‘Quasars’ ji) State and explain Hubble's Law ed by CamScanner

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