PAPER 1

QUESTION 2: a) State and prove Stoke's Theorem
b) Prove that if the vector is a gradient of a scalar function then its line integral around a closed curve is zero.
c) A particle moving along a curve x=2t^2, y= t^2 - 4t, z= 3t-5 where t is the time. Find the components of its velocity and acceleration at time t=1 in the direction 2i-3j+2k.


QUESTION 3: a) What is moment of inertia? State and prove parallel axis theorem.
b) Calculate rotational inertia of a hollow cylinder about cylindrical axis.

QUESTION 4: a) State and prove the Kepler's Laws of areas and Periods of planetary motion.

b) A satellite orbits at a height of 230km above the earth. What is the period of the satellite?

c) At what altitude above the earth surface the value of 'g' is three-quarters of its value at the surface of the earth.

QUESTION 5: a) What is diffraction grating? Explain how grating diffracts light? Derive relation for resolving power of grating.
b) What is meant by polarization of light? How can we get a plane-polarized light by a polarizing sheet?

QUESTION 6: a) Derive equation of Lorentz velocity transformations and show that the speed of light is independent of the relative motion between the frames of reference.
b) The siren of the police car emits a source tone at a frequency of 1125 Hz. Find the frequency that you receive in your car under the following circumstances.
i) Your car is at rest, police car moving towards you at 29 m/s.
ii) Police car at rest, your car moving towards it at 29 m/s.
iii) Your and police car are moving towards one another at 14.5 m/s
iv) Your car moving at 9 m/s, police car chasing behind you at 38 m/s.

QUESTION 7: a) Define Entropy. State Second Law of Thermodynamics in terms of Entropy.
b) Discuss applications of the first Law of Thermodynamics.
c) discuss briefly the Lissajous patterns

QUESTION 8: Explain any FOUR of the following:

a) Doppler's Effect
b) Bernoulli's Theorem
c) Newton's Rings
d) He-Ne Gas LASER
e) Brownian Motion

QUESTION 2: a) Define Electric Field Intensity E. State its value for a point charge and give its units.
b) State differential form of Gauss's law and from there develop the Poisson and Laplace's equations.
c) A charge of 10( square root 2) Coulomb is located at (3i+4j+5k)m. Calculate the Electric field intensity at a point having position vector (5i+4j+3k)m.

QUESTION 3: a) Differentiate between a series and parallel resonant circuit.
b) Explain the construction and operation of a transformer. What are the energy losses in a transformer? How are they reduced to a minimum?
c) A series LCR circuit contains a coil with L=2.25 H, a capacitor having C= 16 microF and a resistor with R= 50 ohms. Calculate the impedance and phase difference between current and voltage. (Take frequency f= 50 Hz)

QUESTION 4: a) State and explain basic postulates of Quantum Physics.
b) Briefly explain with examples what do you mean by Eigen Function and Eigen Values.
c) Derive the time-dependent Schrodinger wave equation for a free particle.

QUESTION 5: a) Why the resistivity of metals increases with temperature but that of the semiconductors decreases?
b) In the process of making semiconductor devices, why silicon is preferred over Germanium?
c) Briefly explain the construction and operation of a Bipolar Junction Transistor (BJT). How can it be used as an Amplifier?

QUESTION 6: a) What do <1 1 1>, [010], (111) and {100} represent for a cubic crystal lattice?
b) What is packing factor? Determine the Atomic Packing Factor of FCC Lattice.
c) With neat diagram showing X-ray Diffraction, derive an expression for Bragg's Law.

QUESTION 7: a) Define Curie and Becquerel. Establish the relation between them.
b) Calculate the decay constant for C-14 which has a half-life of 5730 years.
c) State and explain the Half-Life and Mean life of a radioactive element. Show that <T> is greater than [T1/2].

QUESTION 8: Write short notes on any two of the following:
a) Zeeman Effect
b) Faraday's Law of Electromagnetic Induction
c) Elementary Particles and their Properties.

1. Radius of curvature of the path of a particle in magnetic field can be increased by i) Increasing its velocity ii) Decreasing its velocity iii) Decreasing its magnetic field iv) None of these

2. Mutual Inductance of two coils is maximum when:
i) They are touching ii) They are inclined at 45 degrees to each other. iii) They are inclined at 60 degrees to each other. iv) None of these

3. Compass needle placed near a box shows deflection. the box does not contain a magnet. It contains i) a current carrying conductor

4. Two opposite current-carrying wires will i) attract ii) Repel ii) Do not affect each other iv) None of these

5. Ability to get magnetized is dependent on i) Permeability ii) Permitivity iii) Magnetic Viscosity iv) None of these

6. Pauli exclusion principle is applicable on i) Bossons ii) Fermions

7. For bound particles, the energy states are given as: i) Continuous ii) Degenerate iii) Discrete iv) None

8. Two photons are receding from each other, their relative velocity will be given as i) c ii) 2c iii) c/2 iv) None

9. Both in its cut-off and saturation mode, a transistor acts as a i) Switch ii) Linear Amplifier iii) Variable capacitor iv) None

10. Negative feedback does not improve i) Nonlinear distortion ii) Power Bandwidth iii) Gain Stability iv) None

11. Energy Gap of Si atom is the distance between its valence band and
i) Conduction Band ii

12. Ideal Diode is used for i) Troubleshooting ii) To make precise calculations iii)

13. Inductance is given as i) Flux/Length ii) flux/ current iii) Flux/Area iv) None

14. Isobars are nuclides that have i) Same A and Z ii) Same A different Z iii) Same Z different A iv) None

15. The dipole moment of nucleus will be i) Zero ii) Infinite iii)

16. Liquid drop nucleus model is known as i) Einstein mass-energy relation ii) Mass-velocity model iii) sei-empirical mass model iv) None

17. The shell model purports that the constituent nuclear parts will move

18. The number of atoms per unit cell in fcc is i) 2 ii) 3 iii) 4 iv) None

19. A solid with many small crystalline portions is called i) amorphous solid ii) Crystalline solid iii) Polycrystalline solid iv) None

20. Collective vibrations of an atom are called i) phonons ii) Photons

1. Radius of curvature of the path of a particle in magnetic field can be increased by i) Increasing its velocity ii) Decreasing its velocity iii) Decreasing its magnetic field iv) None of these

2. Mutual Inductance of two coils is maximum when:
i) They are touching ii) They are inclined at 45 degrees to each other. iii) They are inclined at 60 degrees to each other. iv) None of these

3. Compass needle placed near a box shows deflection. the box does not contain a magnet. It contains i) a current carrying conductor

4. Two opposite current-carrying wires will i) attract ii) Repel ii) Do not affect each other iv)None of these

5. Ability to get magnetized is dependent on i) Permeability ii) Permitivity iii) Magnetic Viscosity iv) None of these

6. Pauli exclusion principle is applicable on i) Bossons ii) Fermions

7. For bound particles, the energy states are given as: i) Continuous ii) Degenerate iii) Discrete iv) None

8. Two photons are receding from each other, their relative velocity will be given as i) c ii) 2c iii) c/2 iv) None

9. Both in its cut-off and saturation mode, a transistor acts as a i) Switch ii) Linear Amplifier iii) Variable capacitor iv) None

10. Negative feedback does not improve i) Nonlinear distortion ii) Power Bandwidth iii) Gain Stability iv) None

11. Energy Gap of Si atom is the distance between its valence band and
i) Conduction Band ii

12. Ideal Diode is used for i) Troubleshooting ii) To make precise calculations iii)

13. Inductance is given as i) Flux/Length ii) flux/ current iii) Flux/Area iv) None

14. Isobars are nuclides that have i) Same A and Z ii) Same A different Z iii) Same Z different A iv) None

15. The dipole moment of nucleus will be i) Zero ii) Infinite iii)

16. Liquid drop nucleus model is known as i) Einstein mass-energy relation ii) Mass-velocity model iii) sei-empirical mass model iv) None

17. The shell model purports that the constituent nuclear parts will move

18. The number of atoms per unit cell in fcc is i) 2 ii) 3 iii) 4 iv) None

19. A solid with many small crystalline portions is called i) amorphous solid ii) Crystalline solid iii) Polycrystalline solid iv) None

20. Collective vibrations of an atom are called i) phonons ii) Photons

two wires carrying current in opposite direction repel each other...