PAPER H101 MECHANICS & GENERAL PROPERTIES OF MATTER Total Marks- 35 Pass marks -- 12 Group A Dynamics and Kinematics...
PAPER H101
MECHANICS & GENERAL PROPERTIES OF MATTER
Total Marks- 35 Pass marks -- 12
Group A Dynamics and Kinematics
Dynamics: Inertial and non inertial frame of reference. Transformation equation of coordinate, velocity, acceleration in rotating frame of reference. Radial and transverse velocities of a rotating body. Radial and transverse accelerations. Transformation equation of force in noninertial frames ( both rotational and linear). Fictitious forces -- centrifugal force and Coriolis force. Effect of fictitious force on the earth, Focault’s pendulum . Conservative force and its properties. Concept of potential function. Relationship of conservative force, Motion of a body in fractional medium under gravity.
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. Moment of inertia. Theorems of moment of inertia, calculation of moment of inertia in simple cases : Spherical shell, solid sphere, cylinder, uniform rectangular lamina.
Group B Gravitation and Properties of matter
Elasticity : Relation between elastic constants, energy of elastically deformed bodies, torsion of a rod, Torsional pendulum, bending of beam, Cantilever (loaded at one end).
Surface tension : Excess pressure on curved liquid surface ( spherical bubble and drop). Theory and experimental determination of surface tension of liquid by ripple method.
Viscosity of fluids: Poiseulle’s equation, determination of viscosity of a liquid by Poiseulle’s method.
PAPER H102
MATHEMATICAL PHYSICS I.
Total Marks-35
Pass marks : 12
Group A Co-ordinate System and Vectors
The Co-ordinate system : Orthogonal and non-orthogonal, Right handed and Left Handed Cartesian system, Necessity for curvilinear co-ordinate system. Polar, cylindrical and general curvilinear coordinate system. Length, area and volume elements in all these systems.
Vectors : Vector triple product, polar and axial vectors and their examples from Physics. Vectorial equation of straight line, plane and circle. Base vector, vector transformations. Scalar and vector fields with illustrations from Physics, directional derivative of a scalar field, gradient of a scalar field, divergence and curl of vector fields and their physical meaning, Expression for gradient, divergence and curl in curvilinear co-ordinates. Integration, important identities. Gauss, Green and Stoke’s theorems and their applications.
Group B Matrices , special functions and Fourier series
Matrices : Addition law of matrices, matrix multiplication, properties of matrices, special square matrices, inverse of matrices, Elementary transformation of matrices – similarity, orthogonal and unitary transformation. Eigen value, Eigen vector. Solution of simultaneous linear equations. Diagonalisation of matrix.
Special functions: Beta and Gamma functions, relation between them, recurrence relation for gamma function.
Fourier Series: Fourier’s Theorem and Fourier series, application of Fourier’s theorem to square wave and saw tooth wave
PAPER H 103
GEOMETRICAL OPTICS, WAVES & OSCILLATIONS
Total marks : 35
Pass Marks :12
Group A: Geometrical Optics
Fermat’s principles. Deduction of laws of reflection and refraction using Fermat’s principle for plane and curved surfaces. Deduction of lens maker’s formula.
Thick lens : cardinal points (deduction not necessary). Focal length of two thin lenses separated by a distance.
Defects of image: monochromatic aberration and chromatic aberration, Different types of monochromatic aberration and their explanation. Chromatic aberration and its correction, Achromatic combination of lens & prism.
Spherical aberration and its removal by different methods. Condition of least spherical aberration when two lenses are employed. Aplanatic surface and aplanatic points. Explanation of transparent sphere as aplanatic surface, Extension of the above idea in construction of Abbe’s high power oil immersion objective of microscope.
Different types of magnifications : Transverse, longitudinal, angular and their relationship. Deduction of Helmholtz-Lagrange’s equation and Abbe’s sine condition.
Eyepiece : Ramsden and Huygen eyepiece-construction, principles and relative advantage and disadvantage.
Group B : Waves and Oscillations
Simple harmonic motion: Simple harmonic oscillation - differential equation and its solution Instantaneous and average total energy. Superposition of two simple harmonic motions, Lissajous figures. Damped and forced vibrations. Energy of damped and forced vibrations, Instantaneous and average power of forced vibration, Sharpness of resonance,
Wave: Linear equation of plane progressive wave motion in one and three dimension, Instantaneous and average energy of one dimensional wave, Propagation in dispersive medium – Group and phase velocity
Vibration of strings: Wave equation in linear approximation, Eigen values and eigen functions of pluck and stuck string, Energy of transverse vibration.
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