UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN Physics
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester III - Paper III - Mechanics and Mathematical Methods

Duration of Examination: 3 hrs
Maximum Marks: 100
Credits: 4

Unit I

Impulse and Impact:

Impulse - impact - Laws of impact - direct impact and oblique impact between two smooth spheres - loss of kinetic energy - motion of two interacting bodies - reduced mass.

Mathematical Physics

Characteristic equation of a matrix - eigenvalues - eigenvectors - Diagonalisation of 3x3 real Symmetric matrices - Special functions - Gamma and Beta functions - series solutions for Bessel and Hermite equations.

Unit II

Dynamics of rigid bodies:

Compound pendulum - theory - equivalent simple pendulum - reversibility of centres of oscillation and suspension - determination of g and k - Centre of mass - velocity and acceleration of centre of mass - determination of motion of individual particle - system of variable mass - equation for a rocket - conservation of linear and angular momentum.

Unit III

Gravitation, Centre of gravity and centre of pressure:

Newton's law of gravitation - Boy's method of determination of G - Kepler's laws - orbital velocity and escape velocity - Geo-stationary and Communication- Satellites Centre of gravity of solid and hollow tetrahedron, solid and hollow hemisphere. Centre of pressure - vertical rectangular lamina - vertical triangular lamina.

Unit IV

Hydrodynamics:

Equation of continuity of flow - venturimeter - Pitot's tube for liquids - Euler's equation for unidirectional flow - Torricelli's theorem - Bernoulli's theorem and applications. Laws of floatation - meta centre - meta centric height of a ship. Atmospheric pressure its variations with altitude - reasons for such variations.

Unit V

Classical mechanics:

Mechanics for a system of particles - Generalised Coordinates -transformation equations - configuration space - principle of virtual work - D' Alembert's principle- Lagrange's equation - Hamiltonian function - Hamilton's equation - applications to harmonic oscillator and Kepler problem.

Books for Study:

1. Mechanics - Part I & II by Narayanamoorthy National Publishing company
2. Mathematical Physics - Sathya Prakash
3. Classical Mechanics - H. Goldstein, Addision wesley publication
4. Statistical Mechanics - Sathya Prakash & C. Agarwal Kedarnath & Ramnath & Co. VII edition.

Books for Reference:

1. Mechanics - D.S. Mathur- S.Chand & co, II Edition, 2001.

2. Mathematical Physics - B.D. Gupta.

3. Advanced Engineering mathematics 8^th Edition by Kreyszig.E, Wiley Publ. NY 1989.

4. Mathematical Physics by Ghatak A.K., Gayal LC.. Chaira S.G., MacMillan, New Delhi, 1995.

5. Fundamentals of Physics, 6^th Edition, by D.Halliday, R.Resnick and J.Walker, Wiley, NY, 2001.

6. Physics, 4^th Edition, Vols I, II, & II Extended by D.Halliday, R.Resnick and K.S.Krane, Wiley, NY, 1994.

7. CRC Handbook of Physics & Chemistry, 80^th Ed., CRS Press, NY, 1999.

8. The Feynman Lectures on Physics, Vols. I, II, and III, by R. P. Feynman, R B Leighton and M Sands, Narosa, New Delhi, 1998.