A. MECHANICS
Mechanics of a Single Particle: Velocity and acceleration of a particlein (i) plane polar coordinates - radial and cross-radial components (ii) spherical polar and (iii) cylindrical polar co-ordinate system; Time and path integral of force; work and energy; Conservative force and concept of potential; Dissipative forces; Conservation of linear and angular momentum.
Mechanics of a System of Particles: Centre of mass, centre of mass frame, centre of moving systems, Collision: elastic and inelastic collision, coefficient of restitution. Expression of velocities of two bodies after elastic and inelastic collision in laboratory frame. Elastic collision in centre of mass frame. Relationship between angle of scatterings in laboratory frame and centre of mass frame. Motion of a rigid body about a fixed axis. Angular momentum and expression of angular momentum of a system of rotating bodies. Relationship of angular momentum of a system of bodies with angular momentum in centre of mass frame. Principle of conservation of angular momentum.
Rotational Motion: Moment of inertia, radius of gyration; Energy and angular momentum of rotating systems of particles; Parallel and perpendicular axes theorems of moment of inertia; Calculation of moment of inertia for simple symmetric systems; Ellipsoid of inertia and inertia tensor; Setting up of principal axes in simple symmetric cases. Rotating frames of reference - Coriolis and centrifugal forces, simple examples. Force free motion of rigid bodies - free spherical top and free symmetric top.
B. PROPERTIES OF MATTER
Gravitation: Gravitational potential and intensity, calculation of gravitational potential and intensity due to thin spherical shell, thick spherical shell, sphere, circular disc etc. Compound pendulum, measurement of ‘g’ by bar and Kater’s pendulum.
Elasticity: Hooke's law, work done in strain, elongation strain, volume strain, shearing strain, Young's modulus, Bulk modulus and rigidity modulus and their inter-relationship, Poisson’s ratio, torsion in a cylinder, twisting couple, variation of strain along its length. Bending of beams and cantilevers in different cases: loaded at free end, loaded uniformly, bending moments.
Viscosity: Equation of continuity, Energy of a liquid in flow, Bernoulli's theorem, critical velocity, Reynold's number, Poiseuille's equation, motion in a viscous medium: Stoke's law, streamline and turbulent flow.
Surface tension: Surface tension as a molecular phenomenon, surface tension and surface energy. Excess pressure on curved liquid surface ( spherical bubble and drop). Theory and experimental determination of surface tension of liquid by ripple method.
C. RELATIVITY
Introduction: Galilean transformation and invariance of Newton's laws of motion, non-invariance of Maxwell's equations. Michelson-Morley experiment and explanation of the null result.
Special Theory of Relativity: Concept of inertial frame. Postulates of special theory; simultaneity; Lorentz transformation along one of the axes – length contraction, time dilatation and velocity addition theorem, Fizeau’s experiment. Four vectors. Relativistic dynamics : variation of mass with velocity; energy momentum relationship.
Vectors and Tensors: Covariant and contravariant vectors. Contraction. Covariant, contravariant, and mixed tensors of rank-2, transformation properties. The metric tensor (flat space-time only). Raising and lowering of indices with metric tensors. (Consistent use of any one convention --- diag(-1,1,1,1) or diag(1,-1,-1,-1).) Example of common four-vectors: position, momentum, derivative, current density, four-velocity.
Post a Comment