**Time- 3 Hours**

**Maximum Marks- 100**

**Module – 1**

Q.1. a) Give the theory of forced vibrations and obtain the expression for amplitude. [08 M}

b) With a neat diagram, explain the construction and working of Reddy tube. Mention four applications of shock waves. [08 M]

c) Calculate the resonant frequency for a simple pendulum of length 1 m. [04 M]

OR

Q.2. a) Define force constant and mention its physical significance. Derive the expression for force constant for springs in series and parallel combination.[08 M]

b) Define simple harmonic motion. Derive the differential equation of motion for it using Hook’s law. Mention the characteristics and examples of simple harmonic motion. [08 M]

c) The distance between the two pressure sensors in a shock tube is 150 mm. The time taken by a shock wave to travel this distance is 0.3 ms. If the velocity of sound under the same condition is 340 m/s. Find the mach number of the shock wave. [04 M]

**Module-2**

Q.3. a) Explain longitudinal stress, longitudinal strain, volume stress and volume strain. Discuss the effect of stress temperature, annealing and impurities on elasticity.[08 M]

b) Derive the relation between bulk modulus (k), Young’s modulus (Y) and Poisson’s ratio (α), What are the limitting values of Poisson’s ratio? [08 M]

c) Calculate the extension produced in a wire of length 2m and radius 0.013 × 10^{-2} m due to a force of 14.7 Newton applied along its length. Given, Young’s modulus of the material of the wire Y= 2.1 × 10^{11} N/m^{2}

Q.4. a) Describe a single cantilever and derive the expression for Young’s modulus of the material of rectangular beam. [08 M]

b) Derive an expression for couple per unit twist for a solid cylinder with a diagram. [08 M]

c) Calculate the angular twist of a wire of length 0.3 m and radius 0.2 × 10 ^{-3} m when a torque of 5 ×10^{-4} Nm is applied. (Rigidity modulus of the material is 8 × 10^{10} N/m^{2}). [04 M]

**Module-3**

Q.5. a) explain divergence and curl. Derive Gauss divergence theorem. [08 M]

b) define V-number and fractional index change. With a neat diagram, explain different types of optical fibres. [08 M]

c) Find the divergence of the vector field. \overrightarrow{A}=6x^{2}\widehat{a_{x}}+3xy^{2}\widehat{a_{y}}+xyz^{3}\widehat{a_{z}} at a point P(1,3,6). [04 M]

OR

Q.6. a) derive the expression for displacement current. Mention four Maxwell’s equations in differential form for time varying fields. [08 M]

b) Derive an expression for numerical aperture in an optical fiber and strain the conditions for propagation. [08 M]

c) Find the attenuation in an optical fiber of length 500 m when a light signal of power 100 mW emerges out of the fiber with a power 90 mW. [04 M]

**Module-4**

Q.7.a) State and explain Heisenberg’s Uncertainty principle. Show that the electron cannot exist inside the nucleus. [08 M]

b) Define spontaneous emission and stimulated emission. Explain the construction and working semiconductor laser. [08 M]

c) A partied of mass 0.5 meV/C2 has kinetic energy 100 eV. Find its de Broglie wavelength, where C is the velocity of light. [04 M]

OR

Q.8. a) Assuming the time independent Schrodinger wave equation, discuss the solution for a particle in one dimensional potential well of infinite height. Hence obtain the normalized wave function. [08 M]

b) Derive the expression for energy density interns Einstein’s co-efficient. [08 M]

c) The ratio of population of two energy levels is 1059× 10 -30 . Find the wavelength of light emitted by spontaneous emissions at 330 K. [04 M]

**Module 5**

Q.9. a) Give the assumptions of quantum free electron theory. Discuss two success of quantum free electron theory. [08 M]

b) what are polar and non-polar dielectrics? Explain types of polarisation. [08 M]

c) Calculate the probability of an electron occupying an energy level 0.02 ev above the Fermi level at 200 K and 400 K in a material. [04 M]

OR

Q.10. a) Define internal field. Mention the expressions for internal field, for one dimension, for three dimensional and Lorentz field for dialectics. Derive Clausius- Morsotti equation. [08 M]

b) Describe Fermi level in an intrinsic semi conductor and hence obtain the expression for fermi energy in terms of energy gap of intrinsic semiconductor. [08 M]

c) An elemental solid dielectric material has polarizability 7 × 10 ^{-40} Fm^{2} . Assuming the internal field to be Lorentz field, calculate the dielectric constant for the material if the material has 3 × 10^{28} atoms/m^{3}. [04 M]

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