Name of the University : Mahatma Gandhi University
Department : Applied Physics
Degree : M Sc Physics
Subject Code/Name : PH1C02/Classical Mechanics
Paper : IV
Sem : I
Website : mgu.ac.in
Document Type : Model Question Paper
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/mgu.ac.in/5214-GM%20classical-mechanics-model%20Genral%20QP.pdf
MGU Classical Mechanics Question Paper
Mahatma Gandhi University Kottayam :
First Semester MSc. Degree Examination :
Model question paper :
Related : MGU APH1C03 Solid State Physics M.Sc Model Question Paper : www.pdfquestion.in/5211.html
PH1C02-Classical Mechanics :
Time: 3 hrs Total weightage: 30
Part A (Answer any 6 questions, weightage-1)
1. State the Hamiltonian conservation theorem.
2. State and explain the least action principle.
3. Derive the relationship between Poisson bracket and Lagrange bracket.
4. How does the short wavelength limit of Schroedinger equation leads to Hamilton- Jacobi equation?
5. Discuss the nature of Coriolis’ force.
6. What are the advantages of Hamiltonian formalism over Lagrangian formalism?
7. State the Kepler’s laws of planetary motion.
8. Outline the principle of equivalence.
9. What is meant by a linear system and a non linear system?
10. What is Lyapunov exponent? What is its significance?
Part B : (Answer any 4 questions, weightage-2)
11. Using Hamilton’s equations, show that the angular momentum is conserved in a central force problem.
12. Using Poisson brackets, check whether the transformation defined by q = 2P sinQ, p = 2P cosQ is canonical.
13. Prove that the rotational kinetic energy is conserved in the torque free motion of a rigid body.
14. For a diatomic molecule consisting of masses m1 and m2 connected by a spring of force constant k vibrating along the line joining the masses, determine the normal frequencies and normal co-ordinates.
16. Calculate the fractal dimensions of Cantor set and Sierpinski gasket.
Part C : (Answer all questions, weightage-4)
17 (a) Obtain the Lagrangian for a charged particle moving in an electromagnetic field.
What do you mean by the term, Rayleigh’s dissipation function?
OR
(b) What is Hamilton’s principle? Obtain Lagrange’s equations from Hamilton’s principle using the calculus of variation.
18 (a) Obtain the Lagrange’s equations for small oscillations of a system of two coupled oscillators in the neighborhood of stable equilibrium. Obtain the normal modes and the normal co-ordinates.
OR
(b) (i) Derive Hamilton Jacobi equation. What is Hamilton’s principal function? (ii).
Solve the problem of Harmonic oscillator by Hamilton-Jacobi method.
19. Derive the equation for the orbit of a particle moving under the influence of an inverse square central force field.
OR
(b). Discuss the precessional motion with and without nutation of a spinning symmetrical top under gravity.
20. (a). (i). Derive Einstein’s field equations. (ii). Write a note on gravitational red shift.
OR
(b) Discuss the phase portraits of (i) damped harmonic oscillator (ii) simple pendulum
V Semester :
B. Sc. Physics -Instrumentation (Model III)
PH5D01.1U- Amateur Astronomy
Instructions
1. Time allotted for the examination is 3 Hours.
2. Answer all questions in Part A. This contains 4 bunches of 4 objective type questions. For each bunch, Grade A will be awarded if all the 4 questions are correct, B for 3, C for 2, D for 1 and E for 0. Answer any 5 questions from Part B, any 4 from Part C and any 2 from Part D.
3. Candidates can use ……………………….(type of calculator/tables)
Sample Questions
Part A : (Objective type- weight 1 each)
Bunch I :
Fill in the blanks
1.Among all planets of the solar system, …………. …….. has the most elaborate ring system.
2. Solar eclipses occur when moon’s shadow falls on ….. …
3.According to Ptolemy … ….. is at the centre of the universe.
4.There is an upper limit to the mass of a white dwarf and it is called … …. …. limit..
Bunch II :
Match the following
5. 1.Orion- the hunter a) Constellation
6. 2.Copernicus b) Star cluster
7. 3.Sirius c) Bright star
8. 4.Pleiades d) Heliocentric theory
e) Galaxy
Bunch III :
State whether True/False
9. 1.The stars that we see with our naked eyes belong to our own galaxy.
10.2 Everything in the universe is expanding.
11.3 A star of apparent magnitude 2 will appear brighter than a star of magnitude 4.
12.4 Galileo was the first person to make a telescope.
Bunch IV :
Choose the correct option.
13.1 One parsec is equal to … light-years.
a) 1 b) 3.26 c) 4 d) 2.2 million
14.2 Largest moon (natural satellite) in the solar system is
a) Charon b) Titan c) Triton d) Ganymede
15.3 Penzias and Wilson were awarded Nobel Prize for their discovery of
a) Pulsars b) Redshift c) Black holes d) Cosmic Microwave Background
16.4 Solar system planet with the highest surface temperature is
a) Mercury b) Venus c) Earth d) Mars