UPCMET 2015 Physics Syllabus

Physics

(a) Measurement and Kinematics

1. Estimation of percentage error in the result of an experiment

2. Dimensional analysis: Dimension of a physical quantity M,L,T, θ, (Temperature), Dimensional balance of any equation.

3. Motion along straight line path: Time displacement, time-velocity and time-acceleration graphs. Inter relationship among the graphs.

4. Motion in a plane: Vector addition and subtraction (Laws of Polygon to be used) (AB+BC=AC), Graphical deduction has to be emphasized. Multiplication of a vector by a scalar. Uniform motion on a circular path magnitude of centripetal acceleration and force (Centrifugal force does not exist in inertial frame). Motion under a uniform acceleration along a direction other than that of the initial velocity (motion of projectile under gravity is included herein interpretation of the vector form of the equation v=u + at and s = ut + ½ at².

(b) Mechanics

1. Newton’s Laws of Motion: the first law (Galileo’s Law of Inertia) and the third law (F₁₂ = -F₂₁ ) are obtained from 12 21 the second law (a=F/m), variable force, impulse (F.∆t), conservation of momentum, Principle of jet propulsion.

2. Rotatory motion of a rigid body: Torque, angular acceleration, moment of inertial I=∑mr² = (torque/angular acceleration), angular momentum.

3. Work Energy:  Derivation of expression for kinetic energy (1/2mV²) and (1/2Iω²) respectively from work done by a force and by a couple. Potential energy for a general Fx relation (using the method of area under the curve) for a constant force (e.g.mgh) and for spring 1/2kx² . Conservation of mechanical energy. Elastic and Inelastic collisions (no description). Law of mechanical energy in Inelastic collisions.

4. Universal Gravitation: Motion of planets Kepler’s laws. Law of gravitation in terms of central force dependence of force on an inverse of square of distance (no derivation). Planets, orbital motion and time period, concepts of weightlessness. Gravitational field (nt/Kg) and potential (J/Kg). Height attained by the projectile, escape velocity.

5. Simple harmonic motion: Pure kinetic motion in terms of projection of uniform circular motion. Formula y=A sinωt. Magnitude of acceleration is -ω² times the displacement, kinetic description that motion in which the force is k times the displacement Relation ω² = k/m and t = 2∏√ m/k and its uses in (i) Simple Pendulum (ii) Oscillation in an ideal spring. Time displacement graph, time period, frequency, phase. Total energy in terms of square of amplitude, conversion of energy in the form of potential and kinetic energies, dissipation and damping.

6. Forced oscillation and resonance: Elementary concept of forced oscillations, cases of resonance examples from mechanics, sound and radio etc.

(c) Wave Motion and Sound

1. Speed of mechanical waves: Newton’s formula v=E√d (no derivation) for longitudinal waves. Order of magnitude of v in various media. Application to gases, Laplace’s correction, effect of temperature and pressure for waves on string v =(√T/m) (no derivation).

2. Progressive wave : Equation for a simple harmonic progressive wave, phases and phase difference, Wave front graphical representation of particle velocity against x and t. Qualitative picture of pressure variations in longitudinal waves, intensity dependence on square of amplitude (no derivation).

3. Reflection and refraction of waves: Demonstration of characteristics of wave motion with the help of pulse on a string and on water. Mutual independence of various waves in the same medium. Partial reflection and transmission at the interface of two media, Explanation of reflection and refraction on the basis of secondary wavelets and new wave fronts : sin i₁ /sin i₂ = v₁/v₂

4. Superposition of waves: Interference in space due to two sources, phenomenon of beats, beat frequency equals the difference of parent frequencies.

5. Stationary waves: Bounded medium, stationary waves, nodes and antinodes, Characteristic frequencies of vibration of a bounded medium. Cases of string and air columns (excluding end correction etc.) Sonometer, Melde’s experiment, Resonance column and Kundt’s tube.

6. Doppler’s Principle: Doppler Effect due to the motion of the source and due to the motion of the observer.

(d) General Properties of Matter

1. Kinetic theory and ideal gases: Molecular agitation, deduction of pressure of an ideal gas, Boyle’s Law. Kinetic theory concepts of thermal equilibrium and temperature, Perfect gas equation, deviation from the ideal gas equation at high pressure and low temperature, concepts of finite size of molecules and their mutual interactions. Distinction between gas and vapour, critical temperature.

2. Kinetic models for liquids and solids : Intermolecular forces and potential energy curve. Molecular models for the liquids and solids, Elementary explanation for thermal expansion, fusion. Vaporization, boiling and latent heats.

3. Elasticity : Longitudinal strain, stress and modulus of elasticity. Explanation on the atomic models of solids. Estimation of interatomic force constant. Bulk modulus and rigidity (Only elementary ideas).

4. Surface tension : Surface tension, surface energy. Elementary explanation on the basis of inter molecular forces. Rise of liquid in a capillary tube.

5. Flow of liquids : Ideal fluids, Bernaulli’s equation and its application. Viscous fluids (elementary concepts only), Viscous force on a solid moving in fluid, Stake’s Principle (no derivation), terminal Velocity.

(e) Heat :

1. Thermometry: Constant Volume gas thermometer, Principles of Resistance Thermometer Rt =R0(1+ αt) and t 0 principle of the thermocouple thermometer, Range of various thermometers, Brief explanation of the various other principles used in thermometry. Total radiation, pyrometer and vapour pressure thermometer.

2. First law of thermodynamics : work done by a system = pdv. Definition of the internal energy function U from the relation dU=dQ-pdv. First law of thermodynamics. U a unique function of any state. Distinction between C_p and C_v. Derivation of C_p C_v =R for an ideal gas. General features of the function U. Transitional kinetic energy, v  v intermolecular potential energy, internal rotation and vibration in polyatomic molecules and lattice vibrations.

3. Isothermal and Adiabatic Processes : Definitions, Isothermal elasticity of ideal gas. Adiabatic relationship pvγ = constant (no derivation), adiabatic elasticity of an ideal gas.

4. Thermal Conduction: Elementary concepts of isothermal surface and temperature gradient. Thermal conductivity and one dimensional heat flow in the steady state, kinetic model of thermal conductivity (including metals).

(f) Light

1. Refraction at spherical surfaces: Refraction at spherical surfaces. Derivation of the expression for u, v relationship for refraction at a single spherical surface and a thin lens, (Sign conventions of coordinate geometry to be followed) Newton’s formula xx’ = ff’, combination of lens.

2. Chromatic aberration: Dispersive power of a material, Longitudinal chromatic aberration in a lens, Achromatic combination two lenses in contact.

3. Telescope and Microscope: Astronomical telescope (reflecting refracting types), compounds microscope, magnifying power (for normal eye only). Mention resolving power for both the instruments, need of large aperture telescope and electron microscope (for normal eye only), Mention resolving power for both the instruments, needs of large aperture telescope and electron microscope (no description).

4. Wave nature of light: Elementary observation of diffraction of light by a narrow single slit, comparison with the corresponding observations in ripple tank. Explanation of reflection of lights and refraction of sound on the basis of the wave theory (refer course item c-3). Expression v=c/n. Foucault’s experiment for the measurement of the velocity of light in liquid and its historical significance. Analysis of Young’s experiment, Fringe width, Wavelength of light in various regions of white light. Elementary ideas of plane polarized light, its production and detection (Pile of plates and polorides).

5. Spectrum : formation of spectrum in a prism spectrometer, Minimum deviation and angular dispersion, Ultraviolet and infrared regions of the spectrum, Characteristic properties, complete range of the electromagnetic spectrum: radio wave to gamma rays.

6. Photometry: Luminous intensity of light source at a point in particular direction. Unit candela (cd). Definition of Lumen (Lm)=1 cd sr. An isotropic source of luminous intensity of 1 cd gives a total flux of 4 plm. Rating of a lamp in lumens, candela or watt, Unit lux illumination of a surface (lx)=lumen/meter2, measurement of luminous efficiency in lumens watt, illumination in terms of inverse square law and cosine law. Brief introduction of luminous efficiency, illuminance etc. for various practical cases.

(g) Electricity

1. Electric field and potential: Coulomb’s Law F=q₁ q₂ / (4∏∑₀ r²). Electric field and potential due to a point electric 1 2 o dipole (In longitudinal and transverse position at large distances). Couple acting on a dipole placed in an electric field. Electric field due to a sphere with uniform surface charge density (No Derivation), Proof of atomicity of electric charge. (The procedure of PSSC book to be followed).

2. Capacity: Principle of condenser, capacity of an isolated sphere, a spherical condenser and a parallel plate condenser, effect of dielectric on the capacity. Series and parallel combination of condensers, energy of a charged condenser ½ CV², its comparison with the energy of a stretched spring 1/2Kx².

3. Electric conduction: electric current as a flow of charge carriers. 1 Ampere = 1 coulmb/sec, or 6.25×1018 electronic fundamental charge/sec. Conduction in gases and solutions, concepts of ions, Electrolysis, Faraday’s Laws and Electrochemical equivalent, Faraday’s number, free electrons in metals, carrier density, drift velocity v and relaxation time t Simple derivation of Ohm’s law. Qualitative explanation of the variation of conductivity of normal conductors with temperature. Ohmic and nonohmic circuit elements, Dynamic resistance ∆v/∆i.

4. Simple Circuits: Electric cell as a device which continuously drives charges round a circuit. Electromotive force a characteristic of cell, EMF defined as = W/Q, where W is work done in carrying a charge Q around a closed circuit. Internal resistance of a source (r), Internal potential drop (ir) and power (i²r) Kirchhoffs Laws: series and parallel combination of resistances, Principle of Wheatstone’s bridge, example of meter bridge. Potential divider, Potentiometer.

(h) Electromagnetism

1. Moving charges and magnetic field : Similarities in the behaviour of bar magnet and solenoidal current, measurement of a magnetic field on the basis of force on a linear current F=iBL sin θ, force on a moving charge in a magnetic field Fαqv B sing θ (Lorentz force). Relation between these two expressions, force acting between two parallel linear currents Fαi₁i₂i L/r. Its interpretation on the basis of magnetic field Bi/r Definition of Ampere 1 2 using the expression F=(2×10⁷)i₁ i₂ L/r and definition of the unit of B using the expression F=iBI sin θ. Magnetic 1 2 field at the centre of circular coild and inside a long solenoid (no derivation), Principle of moving coil galvanometer, its conversion into Ammeter and Voltmeter. Principle of D.C. Motor.

2. Magnetism : Couple acting on a bar magnet placed in a magnetic field, magnetic dipole. Definition of magnetic moment on the basis of couple acting in a magnetic field. Electromagnet. Atomic model of magnetism, some atoms have non-zero moment and their alignment gives rise to microscopic magnetism, magnetic field due to a Small bar magnet in longitudinal and transverse positions (2m/d3 and m/d respectively), component of earth’s magnetic field, theories regarding its origin.

3. Electromagnetic Induction : Magnetic flux, its unit weber. 1 weber = I Newton meter/Ampere. Faraday’s law of electromagnetic induction, e=d/dt. Interpretation of induced e.m.f. in terms of Lorentz force. Principle of A.C. and D.C. Dynamos, back e.m.f. in a motor, definition of self inductance (e=-Ldi/dt). Dependence of L on the core material. Graphical description of rise and decay of current in an inductive circuit (no derivation). Definition of mutual inductance (e₂ =-Mdi/dt) and its dependence on the core material. Theory of transformers (qualitative). 2 Microphone (moving coil and carbon type) moving coil loudspeakers.

4. Alternating current circuits: Graphical representation of voltage and current as a function of time, phases difference between V and I. Value of the ratio of V_o /I_o , depends on frequency and the impedance Z for a circuit o o containing only R and L, Z²=R²+ω²L² and tan A=Lω/R (no derivation), root mean square value V_o/√2 and I₀/√2 o power ½ V₀ 1₀ cos θ, choke coil, wattles current. Oscillation in an LC circuit, (Statement only). Frequency of an LC circuit, F=1/2∏√LC (Anology with oscillation of a mass attached to a spring).

(i) Electrons Physics

1. Diode and Triode : Emission of electron from metals on heating, Rectifying action of Diode, Triode and its static mutual characteristics, Triode as an amplifier.

2. Cathode rays and Positive rays : Cathode rays as stream of particles determination of e/m of the particles (using simultaneous electric and magnetic fields) discovery of the electron. Cathode ray oscilloscope (Elementary working principle only), e/m of positive rays, ions isotopes.

3. Photoelectric effect : Photoelectric phenomenon, threshold frequency, Ek is independent of the light intensity, empirical relation E_k = Av-B, where B depends on the cathode surface and A is a universal constant, Einstein’s k explanation of photoelectric effect. A=Planck’s explanation of photoelectric effect. A=Planck’s constant h and B the work function.

(j) Radiation and Atomic Physics :

1. Radiation: Similarly between the nature of radiant energy and lights/Absorptivity, emissivity of surface, Kirchhoffs law, concept of a black body, Stefan’s law, graphical description of spectral distribution of black body radiation (no formulae), elementary ideas of Plank’s hypothesis.

2. Structure of atom : Rutherford’s experiments on particle scattering and his conclusions regarding (i) positively charged nucleus, and (ii) applicability of Coulomb’s law.

3. Origin of spectrum: Experiments of Franck and Hertz, quantized energy states of atoms, energy level diagram, emission and absorptions spectrum, Spectral series of Hydrogen atom, continuous, line and band spectra: their relationship with the state of matter, Fraunhofer lines and their explanation. Fluorescence and phosphorescence.

4. X-ray: Production (Coolidge tube), control on the intensity and penetration, electromagnetic nature of X-rays.

(k) Nuclear Physics

1. Radioactivity: Nature of ab and I rays, concept of half life and statistical nature of the phenomenon of radioactivity. Scintillation screen and cloud chamber respectively for counting and tracking the charged particles (only general features including path tracking by a magnetic field), Composition of nucleus, fundamental particles, e,n,p,∆, p and their antiparticles.

2. Nuclear energy: Nuclear fission, mass defect, mass energy relation ∆E = C²∆m Unification of the principles of conservation of mass and conservation of energy. Principle of nuclear reactor, Elementary ideas of nuclear fusion, origin of solar energy.