# UPTU Previous Year Question Papers

# B Tech 1st Year

# Physics 2006-07

Notes : (i) Attempt all questions.

(ii) Marks carried by the questions are shown against it.

(Hi) The physical constants are given at the end of the question paper.

**1. Attempt any four of the following :**

(a) Using the postulates of special theory of relativity, deduce the Lorentz transformation equations.

(b) Calculate the percentage contraction in the length of rod in a frame of reference, moving with velocity 0.8 c in a direction at an angle of 30° with its length.

(c) A stone is dropped from an aeroplane moving with a constant horizontal velocity. What will be the path (i) as observed by the pilot (ii) as observed by a man standing on the earth ? If both are different then explain why ?

(d) If frame S’ is moving with velocity vi with respect to frame S, and the component of velocity in frame S’ are u’_{x} = c cos(|) and u’_{y} = c sin(|) then prove that for the frame 2S, u_{x}+u_{y} =c .

(e) A spaceship moving away from the earth with velocity 0.5 c fires a rocket whose velocity relative to the space is 0.5 c. Calculate the velocity of the rocket as observed from the earth in following two cases :

(i) away from the earth

(ii) towards the earth

(f) Is there any condition at which the Lorentz transformation reduces to Galilian transformation ? Explain it by taking suitable example.

**2. Attempt any four of the following : **

(a) In a biprism experiment the micrometer reading for zero order and tenth order fringes are 1.25 mm and 2.37 mm respectively when light of X = 5.90 x 10^{-5} cm. is used. Now what will be the position of zero order and tenth order fringes if X is changed to 7.50 x 10^{-5} cm.

(b) Find the expression for the fringe width in case of wedged-straped thin film.

(c) Explain what happens when :

(i) Glass plate is replaced by plane mirror in Newton’s ring experiment

(ii) Thickness of wedged-straped thin film becomes very large.

(iii) A sheet of mica is introduced in the path of one of the interfering wave in Fresnel’s biprism experiment.

(d) What is advantage of oil immersion objective in microscope ? Derive the expression for the resolving power of microscope.

(e) A diffraction grating is just able to resolve two lines ofX = 5140.34 A° and 5140.85 A° in the first order. Will it resolve the lines 8037.20 A° and 8037.50 A° in the second order ?

(f) (i) What are the difference between interference and diffraction ?

(ii) A light of wavelength 5500 A° falls normally on a slit of width22.0x 10^{-5} cm. Calculate the angular position of the first two minima on either side of the central maxima.

**3. Attempt any four of the following :**

(a) What is quarter wave plate ? Describe its method of construction and use. Deduce its thickness for a given wavelength in terms of refractive indices.

(b) Plane polarized light is incident on a plate of quartz cut with faces parallel to optic axis calculate :

(i) the ratio of intensities of extraordinary and ordinary light if the vibrations in the incident light make an angle of 30° with the crystal.

(ii) the least thickness of the plate for which extraordinary and ordinary beams on emergence recombine to form plane polarised light. (Given X = 6000 A°,= 1.5442, (4,^ = 1.5532)5×4

(c) Define the plane of polarization. Give Fresnel’s explanation of the rotation of polarization.

(d) (i) Define the specific rotation

(ii) On introducing a polarimeter tube of 25 cm. long containing a sugar solution of unknown strength it is found that the plane of polarization is rotated through 10°. Find the strength of the solution in gm/cm^{3}. Given specific rotation of sugar solution 60° per decimeter per unit concentration.

(e) (i) Comment on the statement, “Polarization requires that the vibrations are transverse.”

(ii) Can sound waves be polarised ? Give reasons for your answer.

(f) Find the ratio of population of the two states in a He-Ne laser that produces light of wavelength 6328 A^{0} at 27°C. (Given that k (Boltzman constant) is 8.61 x 10^{-5} eV/K)

**4. Attempt any two of the following : **

(a) (i) Explain the concept of displacement current. Write four Maxwell’s equations and explain their physical significance.

(ii) What do you mean by continuity equation and deduce an expression for this equation ?

(b) (i) The relative permittivity of distilled water is 81. Calculate refractive index and velocity of light in it.

(ii) A plane electromagnetic wave propagating along the X-direction has a wavelength 5.0 mm. The electric field is in the y -direction and its maximum magnitude is 38 V/m. Write the equation of the electric and magnetic fields as a function of x and t.

(c) (i) Prove that the energy dissipated per cc. of the magnetisation is |i_{0} times the area of M – H (or I-H) curve.

(ii) Calculate the hourly loss of energy in the iron core of a transformer, the hysterisis loop of which is equivalent in area to 3000 ergs/cm^{3}. Given frequency 50 cycles/sec, density of iron 7.5 gm/cc and weight of the core 12 kg.

**5. Attempt any two of the following : **

(a) Discuss quantum mechanically the problem of linear harmonic oscillator and obtain its eigen values. Also write significance of zero point energy.

(b) What is Compton effect ? Derive an expression h for Compton shift, ^{=} _{m c} ~~ ^{cos} ®) where the symbols are having their usual meanings.

(c) (i) A set of lattice planes reflects X-rays of wavelength 1.32 A^{0} at a glancing angle of 9° 30′. Calculate the possible spacing of this set of planes for different order of reflections. (Given that sin 9° 30′ = 0.1650)

(ii) Compute the energy difference between the ground state and the first excited state for an electron in a one-dimensional rigid box of length 10^{-8} cm. Planck’s constant h = 6.63 x 10^{-34} J.s. Velocity of light in free space c = 3 x 10^{8}m/s Electronic charge e=1.6 xl0^{_19}c Permittivity of free space e_{0}= 8.85×10″ ^{12} F/m Permeability of free space |j,_{0} = 4 % x 10 “^{7} H/m Rest mass of electron m_{e} = 9.1 x 10^{-31} kg