23

7Unit - vII: Properties of Solids and LiquidsElastic behaviour, stress-strain relationship, Hookes law, Youngs modulus, bulk modulus, modulus of rigidity.Pressure due to a fluid column, Pascals law and its applications.Viscosity, Stokess law, terminal velocity, streamline and turbulent flow, Reynolds number, Bernoullis principle and its applications.Surface energy and surface tension, angle of contact, application of surface tension - drops, bubbles and capillary rise.Heat, temperature, thermal expansion, specific heat capacity, calorimetry, change of state, latent heat. Heat transfer-conduction, convection and radiation, Newtons law of cooling.

Unit - vIII: ThermodynamicsThermal equilibrium, zeroth law of thermodynamics, concept of temperature, heat, work and internal energy, first law of thermodynamics.Second law of thermodynamics, reversible and irreversible processes, Carnot engine and its efficiency.

Unit - IX: Kinetic Theory of GasesEquation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases - assumptions, concept of pressure, kinetic energy and temperature, rms speed of gas molecules, degrees of freedom, law of equipartition of energy, applications to specific heat capacities of gases, mean free path, Avogadros number.

Unit - X: Oscillations and WavesPeriodic motion - period, frequency, displacement as a function of time, periodic functions, simple harmonic motion (S.H.M.) and its equation, phase, oscillations of a spring - restoring force and force constant, energy in S.H.M. - kinetic and potential energies, simple pendulum - derivation of expression for its time period, free, forced and damped oscillations, resonance.Wave motion, longitudinal and transverse waves, speed of a wave, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, beats, Doppler effect in sound.Unit - XI: ElectrostaticsElectric charges, conservation of charge, Coulombs law-forces between two point charges, forces between multiple charges, superposition principle and continuous charge distribution.Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in a uniform electric field.Electric flux, Gausss law and its applications to find field due to infinitely long, uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell.Electric potential and its calculation for a point charge, electric dipole and system of charges, equipotential surfaces, electrical potential energy of a system of two point charges in an electrostatic field.Conductors and insulators, dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.

Unit - XII: Current ElectricityElectric current, drift velocity, Ohms law, electrical resistance, resistances of different materials, V-I characteristics of ohmic and non-ohmic conductors, electrical energy and power, electrical resistivity,

8colour code for resistors, series and parallel combinations of resistors, temperature dependence of resistance.Electric cell and its internal resistance, potential difference and emf of a cell, combination of cells in series and in parallel.Kirchhoffs laws and their applications, Wheatstone bridge, metre bridge.Potentiometer - principle and its applications.

Unit - XIII: Magnetic Effects of Current and MagnetismBiot - Savart law and its application to current carrying circular loop.Amperes law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields, cyclotron.Force on a current-carrying conductor in a uniform magnetic field, force between two parallel current-carrying conductors-definition of ampere, torque experienced by a current loop in uniform magnetic field, moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment, bar magnet as an equivalent solenoid, magnetic field lines, earths magnetic field and magnetic elements, para-, dia- and ferro- magnetic substances .Magnetic susceptibility and permeability, hysteresis, electromagnets and permanent magnets.

Unit - XIv: Electromagnetic Induction and Alternating CurrentsElectromagnetic induction, Faradays law, induced emf and current, Lenzs law, Eddy currents, self and mutual inductance.Alternating currents, peak and rms value of alternating current/ voltage, reactance and impedance, LCR series circuit, resonance, quality factor, power in AC circuits, wattless current.AC generator and transformer.

Unit - Xv: Electromagnetic WavesElectromagnetic waves and their characteristics, transverse nature of electromagnetic waves, electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays). Applications of electromagnetic waves..

Unit - XvI: OpticsReflection and refraction of light at plane and spherical surfaces, mirror formula, total internal reflection and its applications, deviation and dispersion of light by a prism, lens formula, magnification, power of a lens, combination of thin lenses in contact, microscope and astronomical telescope (reflecting and refracting) and their magnifying powers.Wave optics - wavefront and Huygenss principle, laws of reflection and refraction using Huygenss principle, interference, Youngs double slit experiment and expression for fringe width, coherent sources and sustained interference of light, diffraction due to a single slit, width of central maximum, resolving power of microscopes and astronomical telescopes, polarisation, plane polarized light, Brewsters law, uses of plane polarized light and polaroids.

Unit - XvII: dual Nature of Matter and radiationDual nature of radiation, photoelectric effect, Hertz and Lenards observations, Einsteins photoelectric equation, particle nature of light.Matter waves-wave nature of particle, de Broglie relation, Davisson-Germer experiment.

9Unit - XvIII: Atoms and NucleiAlpha-particle scattering experiment, Rutherfords model of atom, Bohr model, energy levels, hydrogen spectrum.Composition and size of nucleus, atomic masses, isotopes, isobars, isotones, radioactivity-alpha, beta and gamma particles/rays and their properties, radioactive decay law, mass-energy relation, mass defect, binding energy per nucleon and its variation with mass number, nuclear fission and fusion.

Unit - XIX: Electronic devicesSemiconductors, semiconductor diode - I-V characteristics in forward and reverse bias, diode as a rectifier, I-V characteristics of LED, photodiode, solar cell. Zener diode, Zener diode as a voltage regulator, junction transistor, transistor action, characteristics of a transistor, transistor as an amplifier (common emitter configuration) and oscillator, logic gates (OR, AND, NOT, NAND and NOR), transistor as a switch.

Unit - XX: Communication SystemsPropagation of electromagnetic waves in the atmosphere, sky and space wave propagation, need for modulation, amplitude and frequency modulation, bandwidth of signals, bandwidth of transmission medium, basic elements of a communication system (Block Diagram only).

seCtion BUnit XXi : Experimental SkillsFamiliarity with the basic approach and observations of the experiments and activities: Vernier callipers-its use to measure internal and external diameter and depth of a vessel. Screw gauge-its use to determine thickness/diameter of thin sheet/wire. Simple Pendulum-dissipation of energy by plotting a graph between square of amplitude and

time. Metre Scale - mass of a given object by principle of moments. Youngs modulus of elasticity of the material of a metallic wire. Surface tension of water by capillary rise and effect of detergents. Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical

body. Plotting a cooling curve for the relationship between the temperature of a hot body and time. Speed of sound in air at room temperature using a resonance tube. Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures. Resistivity of the material of a given wire using metre bridge. Resistance of a given wire using Ohms law. Potentiometer (i) Comparison of emf of two primary cells. (ii) Determination of internal resistance of a cell. Resistance and figure of merit of a galvanometer by half deflection method. Focal length of: (i) Convex mirror (ii) Concave mirror, and (iii) Convex lens

10

Using parallax method. Plot of angle of deviation vs angle of incidence for a triangular prism. Refractive index of a glass slab using a travelling microscope. Characteristic curves of a p-n junction diode in forward and reverse bias. Characteristic curves of a Zener diode and finding reverse break down voltage. Characteristic curves of a transistor and finding current gain and voltage gain. Identification of Diode, LED, Transistor, IC, Resistor, Capacitor from mixed collection of such

items. Using multimeter to: (i) Identify base of a transistor (ii) Distinguish between npn and pnp type transistor (iii) See the unidirectional flow of current in case of a diode and an LED. (iv) Check the correctness or otherwise of a given electronic component (diode, transistor or

IC).

CHEMISTrY

Section - A (Physical Chemistry)

UNIT - 1: SOME BASIC CONCEPTS IN CHEMISTrYMatter and its nature, Daltons atomic theory, concept of atom, molecule, element and compound, physical quantities and their measurements in chemistry, precision and accuracy, significant figures, S.I. units, dimensional analysis, Laws of chemical combination, atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae, chemical equations and stoichiometry.

UNIT - 2: STATES OF MATTErClassification of matter into solid, liquid and gaseous states.

Gaseous State - Measurable properties of gases, Gas laws - Boyles law, Charles law, Grahams law of diffusion, Avogadros law, Daltons law of partial pressure, concept of absolute scale of temperature, Ideal gas equation, kinetic theory of gases (only postulates), concept of average, root mean square and most probable velocities, real gases, deviation from Ideal behaviour, compressibility factor, van der Waals equation, liquefaction of gases, critical constants.

Liquid State - Properties of liquids - vapour pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only).

Solid State - Classification of solids - molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea), Braggs Law and its applications, unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, imperfection in solids, electrical, magnetic and dielectric properties.

UNIT - 3: ATOMIC STrUCTUrEDiscovery of subatomic particles (electron, proton and neutron), Thomson and Rutherford atomic models and their limitations, nature of electromagnetic radiation, photoelectric effect, spectrum of

11

hydrogen atom, Bohr model of hydrogen atom - its postulates, derivation of the relations for energy of the electron and radii of the different orbits, limitations of Bohrs model, dual nature of matter, de-Broglies relationship, Heisenberg uncertainty principle, elementary ideas of quantum mechanics, quantum mechanical model of atom, its important features, and 2, concept of atomic orbitals as one electron wave functions, variation of and 2 with r for 1s and 2s orbitals, various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significance, shapes of s, p and d - orbitals, electron spin and spin quantum number, rules for filling electrons in orbitals Aufbau principle, Paulis exclusion principle and Hunds rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals.

UNIT - 4: CHEMICAL BONdING ANd MOLECULAr STrUCTUrEKossel - Lewis approach to chemical bond formation, concept of ionic and covalent bonds.Ionic Bonding - Formation of ionic bonds, factors affecting the formation of ionic bonds, calculation of lattice enthalpy.

Covalent Bonding - concept of electronegativity, Fajans rule, dipole moment, Valence Shell Electron Pair Repulsion (VSEPR) theory and shapes of simple molecules.

Quantum mechanical approach to covalent bonding - valence bond theory - its important features, concept of hybridization involving s, p and d orbitals, Resonance.

Molecular Orbital Theory - its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, concept of bond order, bond length and bond energy.

Elementary idea of metallic bonding, hydrogen bonding and its applications.

UNIT - 5: CHEMICAL THErMOdYNAMICSFundamentals of thermodynamics: system and surroundings, extensive and intensive properties, state functions, types of processes.

First law of thermodynamics - Concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity, Hesss law of constant heat summation, enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution.

Second law of thermodynamics - Spontaneity of processes, S of the universe and G of the system as criteria for spontaneity, G (standard Gibbs energy change) and equilibrium constant.

UNIT - 6: SOLUTIONSDifferent methods for expressing concentration of solution - molality, molarity, mole fraction, percentage (by volume and mass both), vapour pressure of solutions and Raoults law - Ideal and non-ideal solutions, vapour pressure - composition plots for ideal and non-ideal solutions, colligative properties of dilute solutions - relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure, determination of molecular mass using colligative properties, abnormal value of molar mass, vant Hoff factor and its significance.

UNIT - 7: EQUILIBrIUMMeaning of equilibrium, concept of dynamic equilibrium.

12

Equilibria involving physical processes - Solid - liquid, liquid - gas and solid - gas equilibria, Henrys law, general characteristics of equilibrium involving physical processes.

Equilibria involving chemical processes - Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of G and G in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, effect of catalyst, Le Chateliers principle.

Ionic equilibrium - Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius, Bronsted - Lowry and Lewis) and their ionization, acid - base equilibria (including multistage ionization) and ionization constants, ionization of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions. .

UNIT - 8 : rEdOX rEACTIONS ANd ELECTrOCHEMISTrYElectronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions.

Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration: Kohlrauschs law and its applications.

Electrochemical cells - electrolytic and galvanic cells, different types of electrodes, electrode potentials including standard electrode potential, half - cell and cell reactions, emf of a galvanic cell and its measurement, Nernst equation and its applications, relationship between cell potential and Gibbs energy change, dry cell and lead accumulator, fuel cells, corrosion and its prevention.

UNIT - 9 : CHEMICAL KINETICSRate of a chemical reaction, factors affecting the rate of reactions concentration, temperature, pressure and catalyst, elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its units, differential and integral forms of zero and first order reactions, their characteristics and half - lives, effect of temperature on rate of reactions - Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).

UNIT - 10 : SUrFACE CHEMISTrYAdsorption - Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids, Freundlich and Langmuir adsorption isotherms, adsorption from solutions.

Catalysis - Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism.

Colloidal state - distinction among true solutions, colloids and suspensions, classification of colloids - lyophilic, lyophobic, multi molecular, macromolecular and associated colloids (micelles), preparation and properties of colloids - Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation and flocculation, emulsions and their characteristics.

Section - B (Inorganic Chemistry)UNIT - 11: CLASSIFICATION OF ELEMENTS ANd PErIOdICITY IN PrOPErTIESModern periodic law and present form of the periodic table, s, p, d and f block elements, periodic trends in properties of elements atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence, oxidation states and chemical reactivity.

13

UNIT - 12: GENErAL PrINCIPLES ANd PrOCESSES OF ISOLATION OF METALSModes of occurrence of elements in nature, minerals, ores, steps involved in the extraction of metals - concentration, reduction (chemical and electrolytic methods) and refining with special reference to the extraction of Al, Cu, Zn and Fe, thermodynamic and electrochemical principles involved in the extraction of metals.

UNIT - 13: HYdrOGENPosition of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen, physical and chemical properties of water and heavy water, structure, preparation, reactions and uses of hydrogen peroxide, classification of hydrides - ionic, covalent and interstitial, hydrogen as a fuel.

UNIT - 14: s - BLOCK ELEMENTS (ALKALI ANd ALKALINE EArTH METALS)

Group - 1 and 2 ElementsGeneral introduction, electronic configuration and general trends in physical and chemical properties

of elements, anomalous properties of the first element of each group, diagonal relationships.

Preparation and properties of some important compounds - sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate, Industrial uses of lime, limestone, Plaster of Paris and cement, Biological significance of Na, K, Mg and Ca.

UNIT - 15: p - BLOCK ELEMENTS Group - 13 to Group 18 Elements

General Introduction - Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups, unique behaviour of the first element in each group.

Group - 13Preparation, properties and uses of boron and aluminium, structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium chloride and alums.

Group - 14Tendency for catenation, structure, properties and uses of allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites and silicones.

Group - 15Properties and uses of nitrogen and phosphorus, allotropic forms of phosphorus, preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides, (PCl3, PCl5), structures of oxides and oxoacids of nitrogen and phosphorus.

Group - 16Preparation, properties, structures and uses of dioxygen and ozone, allotropic forms of sulphur, preparation, properties, structures and uses of sulphur dioxide, sulphuric acid (including its industrial preparation), Structures of oxoacids of sulphur.

Group - 17Preparation, properties and uses of chlorine and hydrochloric acid, trends in the acidic nature of hydrogen halides, structures of interhalogen compounds and oxides and oxoacids of halogens.

14

Group - 18Occurrence and uses of noble gases, structures of fluorides and oxides of xenon.

UNIT - 16: d - and f - BLOCK ELEMENTSTransition ElementsGeneral introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first row transition elements - physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation, preparation, properties and uses of K2Cr2O7 and KMnO4.

Inner Transition ElementsLanthanoids - Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction.

Actinoids - Electronic configuration and oxidation states.

UNIT - 17: COOrdINATION COMPOUNdSIntroduction to coordination compounds, Werners theory, ligands, coordination number, denticity, chelation, IUPAC nomenclature of mononuclear coordination compounds, isomerism, bonding valence bond approach and basic ideas of crystal field theory, colour and magnetic properties, importance of coordination compounds (in qualitative analysis, extraction of metals and in biological systems).

UNIT - 18: ENvIrONMENTAL CHEMISTrYEnvironmental Pollution - Atmospheric, water and soil. Atmospheric pollution - tropospheric and stratospheric.

Tropospheric pollutants - Gaseous pollutants: oxides of carbon, nitrogen and sulphur, hydrocarbons, their sources, harmful effects and prevention, green house effect and global warming, acid rain.

Particulate pollutants - Smoke, dust, smog, fumes, mist, their sources, harmful effects and prevention.

Stratospheric pollution - Formation and breakdown of ozone, depletion of ozone layer - its mechanism and effects.

Water Pollution - Major pollutants such as, pathogens, organic wastes and chemical pollutants, their harmful effects and prevention.

Soil Pollution - Major pollutants like pesticides (insecticides, herbicides and fungicides), their harmful effects and prevention.Strategies to control environmental pollution.

SECTION - C (Organic Chemistry)

UNIT - 19: PUrIFICATION ANd CHArACTErISATION OF OrGANIC COMPOUNdS

Purification - Crystallization, sublimation, distillation, differential extraction and chromatography - principles and their applications.

Qualitative analysis - Detection of nitrogen, sulphur, phosphorus and halogens.

Quantitative analysis (Basic principles only) - Estimation of carbon, hydrogen, nitrogen, halogens, sulphur, phosphorus.

15

Calculations of empirical formulae and molecular formulae, numerical problems in organic quantitative analysis.

UNIT - 20: SOME BASIC PrINCIPLES OF OrGANIC CHEMISTrYTetravalency of carbon, shapes of simple molecules - hybridization (s and p), classification of organic compounds based on functional groups: C C , C == C - and those containing halogens, oxygen, nitrogen and sulphur, homologous series, Isomerism - structural and stereoisomerism.nomenclature (trivial and IUPAC)

Covalent bond fission - Homolytic and heterolytic: free radicals, carbocations and carbanions, stability of carbocations and free radicals, electrophiles and nucleophiles.

Electronic displacement in a covalent bond - Inductive effect, electromeric effect, resonance and hyperconjugation.

Common types of organic reactions - Substitution, addition, elimination and rearrangement.

UNIT - 21: HYdrOCArBONSClassification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.

Alkanes - Conformations: Sawhorse and Newman projections (of ethane), mechanism of halogenation of alkanes.

Alkenes - Geometrical isomerism, mechanism of electrophilic addition: addition of hydrogen, halogens, water, hydrogen halides (Markownikoffs and peroxide effect), ozonolysis, oxidation, and polymerization.

Alkynes - Acidic character, addition of hydrogen, halogens, water and hydrogen halides, polymerization. Aromatic hydrocarbons - Nomenclature, benzene - structure and aromaticity, mechanism of electrophilic substitution: halogenation, nitration, Friedel Crafts alkylation and acylation, directive influence of functional group in mono-substituted benzene.

UNIT - 22: OrGANIC COMPOUNdS CONTAINING HALOGENSGeneral methods of preparation, properties and reactions, nature of C-X bond, mechanisms of substitution reactions. Uses/environmental effects of chloroform, iodoform, freons and DDT.

UNIT - 23: OrGANIC COMPOUNdS CONTAINING OXYGENGeneral methods of preparation, properties, reactions and uses.

Alcohols - Identification of primary, secondary and tertiary alcohols, mechanism of dehydration.Phenols - Acidic nature, electrophilic substitution reactions: halogenation, nitration and sulphonation, Reimer - Tiemann reaction.

Ethers - Structure.Aldehyde and Ketones - Nature of carbonyl group, nucleophilic addition to >C O group, relative reactivities of aldehydes and ketones, important reactions such as - nucleophilic addition reactions (addition of HCN, NH3 and its derivatives), Grignard reagent, oxidation, reduction (Wolff Kishner and Clemmensen), acidity of -hydrogen, aldol condensation, Cannizzaro reaction, haloform reaction,

16

chemical tests to distinguish between aldehydes and ketones.

Carboxylic acid - Acidic strength and factors affecting it.

UNIT - 24: OrGANIC COMPOUNdS CONTAINING NITrOGENGeneral methods of preparation, properties, reactions and uses.

Amines - Nomenclature, classification, structure basic character and identification of primary, secondary and tertiary amines and their basic character.

diazonium Salts - Importance in synthetic organic chemistry.

UNIT - 25: POLYMErSGeneral introduction and classification of polymers, general methods of polymerization - addition and condensation, copolymerization, natural and synthetic rubber and vulcanization, some important polymers with emphasis on their monomers and uses - polythene, nylon, polyester and bakelite.

UNIT - 26: BIOMOLECULESGeneral introduction and importance of biomolecules.

Carbohydrates - Classification: aldoses and ketoses, monosaccharides (glucose and fructose), constituent monosaccharides of oligosaccharides (sucrose, lactose, maltose) and polysaccharides (starch, cellulose, glycogen).

Proteins - Elementary Idea of - amino acids, peptide bond, polypeptides, proteins - primary, secondary, tertiary and quaternary structure (qualitative idea only), denaturation of proteins, enzymes.

vitamins - Classification and functions.

Nucleic acids - Chemical constitution of DNA and RNA, biological functions of nucleic acids.

UNIT - 27: CHEMISTrY IN EvErYdAY LIFEChemicals in medicines - Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamins - their meaning and common examples.

Chemicals in food - Preservatives, artificial sweetening agents - common examples.

Cleansing agents - Soaps and detergents, cleansing action.

UNIT - 28: PrINCIPLES rELATEd TO PrACTICAL CHEMISTrYDetection of extra elements (N, S, halogens) in organic compounds, detection of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl and amino groups in organic compounds.

Chemistry involved in the preparation of the following:

Inorganic compounds - Mohrs salt, potash alum.

Organic compounds - Acetanilide, p-nitroacetanilide, aniline yellow, iodoform.Chemistry involved in the titrimetric exercises - Acids, bases and the use of indicators, oxalic acid vs KMnO4, Mohrs salt vs KMnO4.

17

Chemical principles involved in the qualitative salt analysis:Cations - Pb2+, Cu2+, AI3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+, NH4+.Anions CO32, S2, SO42, NO2, NO3, CI, Br, I (insoluble salts excluded).Chemical principles involved in the following experiments:1. Enthalpy of solution of CuSO42. Enthalpy of neutralization of strong acid and strong base.3. Preparation of lyophilic and lyophobic sols.4. Kinetic study of reaction of iodide ion with hydrogen peroxide at room temperature.

MATHEMATICS

UNIT - 1 : SETS, rELATIONS ANd FUNCTIONSSets and their representation, union, intersection and complement of sets and their algebraic properties, power set, relations, types of relations, equivalence relations, functions, one-one, into and onto functions, composition of functions.

UNIT - 2 : COMPLEX NUMBErS ANd QUAdrATIC EQUATIONSComplex numbers as ordered pairs of reals, representation of complex numbers in the form a + ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, quadratic equations in real and complex number system and their solutions, relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.

UNIT - 3 : MATrICES ANd dETErMINANTSMatrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

UNIT - 4 : PErMUTATIONS ANd COMBINATIONSFundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.

UNIT - 5 : MATHEMATICAL INdUCTIONPrinciple of Mathematical Induction and its simple applications.

18

UNIT - 6 : BINOMIAL THEOrEM ANd ITS SIMPLE APPLICATIONSBinomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications.

UNIT - 7 : SEQUENCES ANd SErIESArithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: n n n, , , 2 3 . Arithmetic - Geometric progression.

UNIT - 8 : LIMITS, CONTINUITY ANd dIFFErENTIABILITYReal - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions, derivatives of order upto two. Rolles and Lagranges Mean value theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.

UNIT - 9 : INTEGrAL CALCULUSIntegral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.Evaluation of simple integrals of the type3

dxx a

dxx a

dxa x

dxa x

dxax bx c

dxax bx c

px2 2 2 2 2 2 2 2 2 2 + + + +

+, , , , , , ( qq dxax bx c

px q dxax bx c

px q dxax dx c

) , ( ) , ( )2 2 2+ +++ +

++ +

dxx a

dxx a

dxa x

dxa x

dxax bx c

dxax bx c

px2 2 2 2 2 2 2 2 2 2 + + + +

+, , , , , , ( qq dxax bx c

px q dxax bx c

px q dxax dx c

) , ( ) , ( )2 2 2+ +++ +

++ +

a x dx x a dx2 2 2 2 and Integral as limit of a sum. Fundamental theorem of calculus. Properties of definite integrals. Evaluation

of definite integrals, determining areas of the regions bounded by simple curves in standard form.

UNIT - 10: dIFFErENTIAL EQUATIONSOrdinary differential equations, their order and degree. Formation of differential equations. Solution of

19

differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type:dydx

p x y q x+ =( ) ( )

UNIT - 11: COOrdINATE GEOMETrYCartesian system of rectangular coordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.Straight lines - Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.

Circles, conic sections - Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point(s) of tangency.

UNIT - 12: THrEE dIMENSIONAL GEOMETrYCoordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.

UNIT - 13: vECTOr ALGEBrAVectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.

UNIT - 14: STATISTICS ANd PrOBABILITYMeasures of dispersion - Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

Probability - Probability of an event, addition and multiplication theorems of probability, Bayes theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

UNIT - 15: TrIGONOMETrYTrigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.

UNIT - 16: MATHEMATICAL rEASONING

20

Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive.

From the graph shown with each chapters, it is evident that the average chances of questions coming in the AIEEE examination is different for different units. The probability of questions being asked in the examination is maximum for the following units.

Physics Electrostatics Thermodynamics Oscillations and Waves Electromagnetic Induction and Alternating Current Atoms and Nuclei

Chemistry Organic Compounds Containing Oxygen Solutions Equilibrium Chemical Thermodynamics Some Basic Principles of Organic Chemistry p-Block Elements (Group 13 to 18)

Mathematics Limits, Continuity and Differentiability Co-ordinate Geometry Statistics and Probability Matrices and Determinants Integral Calculus

1PH YSI CS

1. Identifythepairwhosedimensionsareequal.(a) torqueandwork (b) stressandenergy(c) forceandstress (d) forceandwork.

(2002)

2. Dimensionsof0 0

1 m e ,where symbols have their

usualmeaning,are(a) [L1T] (b) [L2T2](c) [L2T2] (d) [LT1].

(2003)

3. Thephysicalquantitiesnot havingsamedimensionsare(a) torqueandwork(b) momentumandPlanck'sconstant(c) stressandYoung'smodulus(d) speedand(m0 e0)1/2.

(2003)

4. Whichoneofthefollowingrepresentsthecorrectdimensions of the coefficient of viscosity?(a) ML1T2 (b) MLT1

(c) ML1T1 (d) ML2T2.(2004)

5. Out of the following pairswhich one does nothave identicaldimensions is(a) moment ofinertia andmomentofa force(b) workand torque(c) angularmomentumandPlancksconstant(d) impulseandmomentum

(2005)

6. WhichofthefollowingunitsdenotesthedimensionsML2/Q2,whereQdenotes theelectric charge?(a) weber(Wb) (b) Wb/m2

(c) henry(H) (d) H/m2.(2006)

7. The dimension of magnetic field in M, L, T and C (coulomb) is given as (a) MT 2 C 1 (b) MLT 1 C 1

(c) MT 2 C 2 (d) MT 1 C 1 . (2008)

1 CHAPTER

Units and Measurements

Answer Key

1. (a) 2. (c) 3. (b) 4. (c) 5. (a) 6. (c)7. (d)

JEE MAIN 1

2 C h a p t e r w i s e A I E E E E X P L O R E R

1. (a):Torqueandworkhavethesamedimensions.

2. (c) : Velocity of light in vacuum0 0

1 = m e

or 1

0 0

1[LT ] -

= m e

or 2 20 0

1[L T ] - = m e

\ Dimensions of 2 20 0

1 [L T ] - = m e .

3. (b) : [Momentum]= [MLT1][Planck's constant] = [ML2T1]MomentumandPlanck'sconstantdonothavesamedimensions.

4. (c) :Viscous forceF = 6phrv

\ 6Frv

h = p

or[ ]

[ ][ ][ ]

Fr v

h =

or2

1

[MLT ][ ][L][LT ]

-

- h =

or [h] = [ML1 T1].

5. (a) : Moment of inertia (I)= mr2

\ [I] = [ML2]Moment of force (C) = r F \ [C] = [r][F] = [L][MLT2]or [C]= [ML2 T2]Momentofinertiaandmomentofa forcedonothave identical dimensions.

6. (c) : [ML2Q2]= [ML2A2 T2][Wb] = [ML2 T2 A1]

2 12

Wb = [MT A ]m

[henry] = [ML2 T2 A2]

2 22

H [MT A ]m

- - =

Obviouslyhenry (H) has dimensions2

2ML .Q

7. (d): Lorentz force | | | |F qv B = = r r r

2 2

1 1[ ] MLT MLT[ ][ ][ ] C LT CLT

FB

q v

- -

- - \ = = = =[MT1C1]

JEE MAIN 2

3PH YSI CS

1. Ifabodylooseshalfofitsvelocityonpenetrating3 cm in awooden block, thenhowmuchwill itpenetratemore before coming to rest?(a) 1 cm (b) 2 cm(c) 3 cm (d) 4 cm.

(2002)2. Speedsoftwoidenticalcarsare u and4u ataspecific

instant.Ifthesamedecelerationisappliedonboththe cars, the ratio of the respective distances inwhichthetwocarsarestoppedfromthatinstant is(a) 1:1 (b) 1:4(c) 1:8 (d) 1:16.

(2002)3. Fromabuildingtwoballs A andB arethrownsuch

thatAisthrownupwardsandBdownwards(bothvertically).If vAand vBaretheirrespectivevelocitieson reaching the ground, then(a) vB > vA(b) vA= vB(c) vA> vB(d) their velocities depend on their masses.

(2002)

4. A carmovingwith a speed of 50 km/hr, can bestoppedbybrakes afterat least6m. If thesamecarismovingataspeedof100km/hr,theminimumstoppingdistance is(a) 12m (b) 18m(c) 24m (d) 6m.

(2003)

5. Aballisreleasedfromthetopofatowerofheighthmetre.Ittakes T secondtoreachtheground.Whatis thepositionof the ball in T/3 second?(a) h/9metre from the ground

Description of Motion in One Dimension

2 CHAPTER

(b) 7h/9metre from the ground(c) 8h/9metre from the ground(d) 17h/18metre from the ground.

(2004)

6. An automobile travelling with a speed of60 km/h, can brake to stopwithin a distance of20 m. If the car is going twice as fast, i.e.120km/h, the stoppingdistancewill be(a) 20m (b) 40m(c) 60m (d) 80m.

(2004)

7. The relation between time t and distance x ist = ax2+ bx where a and b are constants. Theacceleration is(a) 2av3 (b) 2av2

(c) 2av2 (d) 2bv3

(2005)

8. A car, startingfrom rest, accelerates at the rate fthrough a distance s, then continues at constantspeed for time t and then decelerates at the ratef/2 tocome to rest. If the totaldistance traversedis 15 s, then

(a)21

2s f t = (b)

21

4s f t =

(c) s= ft (d) 216

s f t =

(2005)

9. Aparachutistafterbailingoutfalls50mwithoutfriction.When parachute opens, it decelerates at2 m/s2. He reaches the ground with a speed of3m/s.Atwhat height, didhebail out?

JEE MAIN 3


(a) 293m (b) 111m(c) 91m (d) 182m

(2005)

10. A particle located at x = 0 at time t = 0, startsmovingalongthepositive xdirectionwithavelocityvthatvariesas .v x = a Thedisplacementoftheparticle varieswith time as(a) t3 (b) t2

(c) t (d) t1/2.(2006)

11. Thevelocityofaparticleisv=v0+gt+ft2.Ifitspositionisx =0att =0,thenitsdisplacementafterunittime(t=1)is(a) v0+g/2+f (b) v0+2g+3f(c) v0+g/2+f/3 (d) v0+g+f

(2007)

12. Abodyisatrestat x =0.At t=0,itstartsmovingin the positive xdirection with a constant

Answer Key

1. (a) 2. (d) 3. (b) 4. (c) 5. (c) 6. (d)

7. (a) 8. nooption 9. (a) 10. (b) 11. (c) 12. (c)

acceleration.At the same instant another bodypasses through x = 0 moving in the positive xdirectionwithaconstantspeed.Thepositionofthefirstbodyisgivenby x1(t)aftertime t andthatof thesecondbodyby x2 (t)afterthe same timeinterval.Whichofthefollowinggraphscorrectlydescribes(x1 x2)asafunctionof time t?

(a)

Ot

( )x x21

(b)

Ot

( )x x21

(c)

Ot

( )x x21

(d)O

t

( )x x21

(2008)

JEE MAIN 4

5PH YSI CS

1. (a): Forfirstpartofpenetration,byequationofmotion,

22 2 (3)

2u u a =

or 3u2 = 24a u2 = 8a ........... (i)For latter part of penetration,

2

0 22u ax =

or u2 =8ax ........... (ii)From (i) and (ii)

8ax = 8a x = 1 cm.2. (d) : Both are given the same deceleration

simultaneously and both finally stop.Formula relevant tomotion : u2 = 2 as

\ For first car,2

1 2usa

=

For second car,2 2

2(4 ) 162 2u usa a

= =

\ 12

116

ss

= .

3. (b) : Ball A projected upwards with velocity ufalls back to building top with velocity udownwards. It completes its journey to groundunder gravity. \ vA2 = u2 + 2gh ..............(i)Ball B startswithdownwardsvelocityu andreachesground after travelling a vertical distance h \ vB2 = u2 + 2gh ............(ii)From (i) and (ii)vA = vB.

4. (c) : For first case,

1km 50 1000 125 m50hour 60 60 9 sec

u = = =

\ Acceleration22

21

1

125 1 16 m/sec2 9 2 6u

as

= - = - = -

For second case,

2km 100 1000 250 m100hour 60 60 9 sec

u = = =

\22

22

1 250 1 24 m2 2 9 16u

sa

- - = = - =

or s2 =24m.

5. (c) : Equation ofmotion : 212

s ut gt = +

\ 210 2h gT = +

or 2h = gT2 ..... (i)After T/3 sec,

2 2102 3 18

gTTs g = + =

or 18 s = gT2 ....... (ii)From (i) and (ii),18 s = 2h

or9hs = m from top.

\ Height fromground = 8 m.9 9h hh - =

6. (d):LetabetheretardationforboththevehiclesFor automobile, v2 = u2 2 as \ u12 2as1 = 0 u12 = 2as1Similarly for car, u22 = 2as2

\2 2

2 2 2

1 1

12060 20

u s su s

= =

or s2 =80m.

7. (a) : t = ax2 + bxDifferentiate the equation with respect to t

\ 1 2 dx dxax bdt dt

= +

or 1 2 asdxaxv bv vdt

= + =

or1

2v

ax b =

+

or 222 ( / )

2(2 )

a dx dtdv av vdt ax b

- = = - +

or Acceleration = 2av3.

8. For first part of journey, s = s1,2

1 112

s f t s = = ............ (i)

v = f t1 ........... (ii)

JEE MAIN 5


For second part of journey,s2 = vtor s2 = f t1 t ........... (iii)For the third part of journey,

23 1

1 (2 )2 2

fs t =

or21

341

2 2f t

s =

or s3 = 2s1 = 2s ............ (iv)s1 + s2 + s3 = 15s

or s + f t1t + 2s = 15sor f t1t = 12s ........... (v)From (i) and (v),

21

112 2fts

s ft t =

or 1 6tt =

or2 2

21

1 12 2 6 72

ftts ft f = = =

or2

72ft

s =

None of the given options provide this answer.

9. (a) : Initially, theparachutist fallsundergravity \ u2 = 2ah = 2 9.850= 980m2s2

He reaches the groundwith speed=3m/s, a = 2ms2

\ (3)2 = u2 2 2 h1or 9=980 4 h1

or 19714

h =

or h1 = 242.75m \ Total height= 50 + 242.75

=292.75=293m.

10. (b) : v x = a

ordx xdt

= a

ordx dtx

= a

ordx dtx

= a

or 1/ 22x t = a

or2

2

2x t a =

or displacement is proportional to t2.

11. (c):Given:velocityv=v0+gt+ ft2

\ dxv dt = or 0 0

x tdx vdt =

or 200

( )t

x v gt ft dt = + + 2 3

0 2 3gt ft

x v t C = + + +

whereCistheconstantof integrationGiven:x=0,t=0. \ C=0

or2 3

0 2 3gt ft

x v t = + +

Att=1sec

\ 0 .2 3g f

x v = + +

12. (c):Asu=0,v1=at,v2=constantfortheotherparticle.Initiallybotharezero.Relativevelocityofparticle1w.r.t.2isvelocityof1velocityof2.Atfirstthevelocityoffirstparticleislessthanthatof2.Then thedistance travelledbyparticle1increasesas

x1=(1/2)at1 2.Fortheseconditisproportionaltot.Thereforeitisaparabolaaftercrossingxaxisagain.Curve(c)satisfiesthis.

JEE MAIN 6

7PH YSI CS

1. Twoforcesaresuchthatthesumoftheirmagnitudesis 18 N and their resultant is 12 N which isperpendicular to the smaller force. Then themagnitudes of the forces are(a) 12N,6N (b) 13N,5N(c) 10N,8N (d) 16N,2N.

(2002)

2. Aboyplayingontheroofofa10mhighbuildingthrowsaballwithaspeedof10m/satanangleof 30 with the horizontal. How far from thethrowing pointwill the ball be at the height of10m fromthe ground ? [g = 10m/s2, sin30 =1/2, cos30 = 3/ 2](a) 5.20m (b) 4.33m(c) 2.60m (d) 8.66m.

(2003)

3. Thecoordinatesofamovingparticleatanytimetaregivenbyx= at3 andy= bt3.Thespeedofthe particle at time t is given by

(a) 2 23t a + b (b) 2 2 23t a + b

(c) 2 2 2t a + b (d) 2 2 a + b .

(2003)

4. If A B B A = r r r r

,thentheanglebetween A and Bis(a) p (b) p/3(c) p/2 (d) p/4.

(2004)

5. A projectile can have the same rangeR for twoangles of projection. If T1 and T2 be the time offlightsinthetwocases,thentheproductofthetwotime of flights is directly proportional to

Description of Motion in 2 and 3 Dimension

3 CHAPTER

(a) 1/R2 (b) 1/R(c) R (d) R2.

(2004)

6. Which of the following statements is false for aparticlemovinginacirclewithaconstantangularspeed?(a) The velocity vector is tangent to the circle.(b) Theaccelerationvectoristangenttothecircle(c) theaccelerationvectorpointstothecentreof

the circle(d) the velocity and acceleration vectors are

perpendicular to each other.(2004)

7. Aball is thrown froma pointwitha speedv0 atanangleofprojection q.Fromthesamepointandatthesameinstantapersonstartsrunningwithaconstantspeed v0/2tocatchtheball.Willthepersonbe able to catch theball? If yes,what should bethe angle of projection?(a) yes, 60 (b) yes, 30(c) no (d) yes, 45.

(2004)

8. Aparticle ismovingeastwardswith a velocity of5 m/s. In 10 s the velocity changes to 5 m/snorthwards.Theaverageaccelerationinthistimeis(a) zero

(b)1

2ms2 towardsnorthwest

(c)1

2ms2 towardsnortheast

JEE MAIN 7

8 C h a p t e r w i s eA I E E E E X P L O R E R

(d)12

ms2 towardsnorth

(2005)

9. A projectile can have the same rangeR for twoangles of projection. If t1 and t2 be the time of

Answer Key

1. (b) 2. (d) 3. (b) 4. (a) 5. (c) 6. (b)7. (a) 8. (b) 9. (b)

flightsinthetwocases,thentheproductofthetwotime of flights is proportional to(a) 1/R (b) R(c) R2 (d) 1/R2.

(2005)

JEE MAIN 8

9PH YSI CS

1. (b):ResultantRisperpendiculartosmallerforceQand (P+ Q)= 18N \ P2 = Q2 + R2 by right angled triangle

P

R90

Q

or (P2 Q2) = R2

or (P + Q)(P Q) = R2

or (18)(PQ)= (12)2 [ 18]P Q + = Qor (P Q)= 8HenceP = 13N and Q = 5N.

2. (d) : Height of building = 10mTheballprojectedfromtheroofofbuildingwillbe back to roof height of 10m after coveringthemaximum horizontal range.

Maximum horizontal range2sin 2( ) uR

g q =

or2(10) sin60

10 0.86610

R

= =

or R = 8.66m.

3. (b) : Q x = at3

\ 2 23 3xdx t v tdt

= a = a

Again y = bt3

\ 23ydy

v tdt

= b \ v2 = vx2 + vy2

or v2 = (3at2)2 + (3bt2)2 = (3t2)2 (a2 + b2)or 2 2 23 .v t = a + b

4. (a) : A B B A = r r r r

or sin sin( )AB n AB n q = -qor sinq = sinqor 2 sinq = 0or q = 0, p, 2p..... \ q = p.

5. (c):Rangeissameforanglesofprojection qand(90 q)

\ 1 22 sin (90 )2 sin anduuT T

g g -q q = =

\2 2

1 2 2

4 sin cos 2 sin2 2u u RT Tg g gg

q q q = = =

\ T1 T2 is proportional to R.6. (b):Theaccelerationvectoractsalongtheradius

of the circle.The given statement is false.

7. (a) :Thepersonwill catch the ball if hisspeedand horizontal speed of the ball are same

= 001cos cos cos60

2 2v

v q = q = = \ q=60.

8. (b) : Velocity in eastward direction 5i =velocity in northward direction 5 j =

45

5ja

W E5i +5i -

N

\ Acceleration 5 510j i

a -

= r

or1 1 2 2

a j i = - r

or2 2

1 1| |2 2

a = + -

r

or 21| | ms2

a - = r towards northwest.

9. (b):Rangeissameforanglesofprojection qand(90 q)

\ 1 22 sin (90 )2 sin anduut t

g g - q q = =

\2 2

1 2 24 sin cos 2 sin 2 2u u Rt t

g g gg q q q = = =

\ t1 t2 is proportional to R.

JEE MAIN 9

11PH YSI CS

1. Theminimumvelocity(inms1)withwhichacardriver must traverse a flat curve of radius150 m and coefficient of friction 0.6 to avoidskiddingis(a) 60 (b) 30 (c) 15 (d) 25.

(2002)

2. Aliftismovingdownwithaccelerationa.Amanintheliftdropsaballinsidethelift.Theaccelerationof theballasobservedby theman in theliftanda man standing stationary on the ground arerespectively(a) g, g (b) g a, g a(c) g a, g (d) a, g.

(2002)

3. WhenforcesF1,F2,F3 areactingonaparticleofmass m such that F2 and F3 are mutuallyperpendicular,thentheparticleremainsstationary.Iftheforce F1isnowremovedthentheaccelerationof the particle is(a) F1/m (b) F2F3/mF1(c) (F2 F3)/m (d) F2/m.

(2002)

4. Oneendof amasslessrope,whichpassesovera massless andfrictionless pulleyP istied toa hookCwhilethe other end is free.Maximum tension thatthe rope can bear is 960N.Withwhat value ofmaximumsafeacceleration(inms2)canamanof60kg climbon the rope?(a) 16 (b) 6 (c) 4 (d) 8.

(2002)

5. A lightstringpassingovera smooth light pulleyconnects two blocks of masses m1 and m2(vertically). If the acceleration of the system isg/8, then the ratio of themasses is(a) 8 : 1 (b) 9 : 7 (c) 4 : 3 (d) 5 : 3.

(2002)

6. Three identical blocks ofmasses m = 2 kg aredrawnbyaforceF=10.2Nwithanaccelerationof 0.6 ms2 on africtionless surface,thenwhatisthetension(in N) in the stringbetween the blocks B and C?(a) 9.2 (b) 7.8 (c) 4 (d) 9.8

(2002)

7. Threeforcesstartactingsimultaneouslyonaparticlemoving with velocity v

r . These forces arerepresented in magnitude anddirection by the three sides of atriangle ABC (as shown). Theparticle will now move withvelocity(a) less than v

r

(b) greater than vr

(c) | vr| in the direction of the largest force BC

(d) vr, remainingunchanged.

(2003)

8. Aspringbalanceisattachedtotheceilingofalift.Amanhangshisbagonthespringandthespringreads49N,when the lift is stationary. If the liftmovesdownwardwithanaccelerationof5m/s2,the reading of the springbalancewill be(a) 24N (b) 74N (c) 15N (d) 49N.

(2003)

4 CHAPTER

Laws of Motion

C

P

A B

C

BC A F

JEE MAIN 10


9. Ahorizontal force of10Nis necessary to just hold ablock stationary against awall. The coefficient offriction between the blockand the wall is 0.2. Theweight of the block is(a) 20N (b) 50N (c) 100N (d) 2N.

(2003)

10. Amarble block ofmass 2 kg lyingon icewhengivenavelocityof6m/sisstoppedbyfrictionin10 s. Then the coefficient of friction is(a) 0.02 (b) 0.03 (c) 0.06 (d) 0.01.

(2003)

11. A block of mass M is pulled along a horizontalfrictionlesssurfacebyaropeofmassm.IfaforcePis applied at thefreeendof therope, the forceexerted by the rope on the block is

(a)Pm

M m + (b)Pm

M m -

(c) P (d) .PM

M m +(2003)

12. Alightspringbalancehangsfromthehookoftheother light spring balance and a block of massM kg hangs from the former one. Then the truestatement about the scale reading is(a) both the scales readM kg each(b) thescaleoftheloweronereadsMkgandof

the upper one zero(c) thereadingofthetwoscalescanbeanything

but the sumof the readingwill be M kg(d) both the scales readM/2 kg.

(2003)

13. Arocketwithaliftoffmass3.5104kgisblastedupwards with an initial acceleration of10m/s2.Then the initial thrust of the blast is(a) 3.5105 N (b) 7.0105 N(c) 14.0 105 N (d) 1.75 105 N.

(2003)

14. Amachinegunfiresabulletofmass40gwithavelocity1200ms1.Themanholding itcanexertamaximumforceof144Nonthegun.Howmanybullets canhe fire per second at themost?

(a) one (b) four (c) two (d) three.(2004)

15. Two masses m1 = 5 kg andm2=4.8kgtiedtoastringarehangingovera light frictionlesspulley.Whatistheaccelerationofthemasseswhenlift free to move?

(g = 9.8m/s2)

(a) 0.2m/s2

(b) 9.8m/s2

(c) 5m/s2

(d) 4.8m/s2.(2004)

16. Ablockrestsonaroughinclinedplanemakinganangle of 30with the horizontal.The coefficientof staticfrictionbetween theblockandtheplaneis0.8.Ifthefrictionalforceontheblockis10N,themassof the block (in kg) is

(takeg = 10m/s2)(a) 2.0 (b) 4.0 (c) 1.6 (d) 2.5

(2004)

17. AnannularringwithinnerandouterradiiR1 andR2isrollingwithoutslippingwithauniformangularspeed.The ratio of the forces experienced by thetwoparticlessituatedontheinnerandouterpartsof the ring, F1/F2 is

(a) 1 (b)1

2

RR

(c)2

1

RR (d)

21

2

R

R

(2005)

18. Asmoothblockisreleasedatrestona45oinclineandthenslidesadistance d.Thetimetakentoslideisntimesasmuchtoslideonroughinclinethanon asmooth incline.Thecoefficientof friction is

(a) 21

1sn

m = - (b) 21

1sn

m = -

(c) 21

1kn

m = - (d) 21

1kn

m = -

(2005)

19. Theupperhalfofaninclinedplanewithinclination f isperfectlysmoothwhilethelowerhalfisrough.Abodystartingfromrestatthetopwillagaincome

m1

m2

10 N

JEE MAIN 11

13PH YSI CS

to rest at the bottom if the coefficient of frictionfor the lower half is given by(a) 2tanf (b) tanf (c) 2sinf (d) 2cosf

(2005)

20. Abulletfiredintoafixedtargetloseshalfitsvelocityafterpenetrating3 cm.Howmuch further itwillpenetrate before coming to rest assuming that itfaces constant resistance to motion?(a) 1.5 cm (b) 1.0 cm (c) 3.0 cm (d) 2.0cm

(2005)

21. Aparticle ofmass 0.3 kg issubjected toa forceF=kxwithk=15N/m.Whatwillbeitsinitialacceleration if it is released from a point 20 cmaway from the origin?(a) 5m/s2 (b)10m/s2 (c) 3m/s2 (d) 15m/s2

(2005)

22. Ablockiskeptonafrictionlessinclinedsurfacewith angle of inclination a.The incline is givenan acceleration a tokeep the blockstationary. Then a isequal to(a) g(b) gtana(c) g/tana (d) gcoseca

(2005)

23. Consider a carmovingona straight roadwith aspeedof 100m/s.Thedistance atwhich car canbe stopped is [mk = 0.5](a) 100m (b) 400m(c) 800m (d) 1000m

(2005)

24. Aplayercaughtacricketballofmass150gmovingat a rate of 20 m/s. If the catching process iscompleted in 0.1s, the forceof theblowexertedby the ball on the handof the player is equal to(a) 300N (b) 150N (c) 3N (d) 30N.

(2006)

25. Aballofmass0.2kgisthrownverticallyupwardsby applying a force by hand. If the handmoves0.2mwhichapplyingthe forceandtheballgoesupto2mheightfurther,findthemagnitudeoftheforce. Consider g = 10m/s2

(a) 22N (b) 4N (c) 16N (d) 20N.(2006)

26. Ablockofmassm isconnectedtoanotherblockofmassM byaspring(massless)ofspringconstant k.Theblocksarekeptonasmoothhorizontalplane.Initially the blocks are at rest and the spring isunstretched.Thenaconstant forceFstartsactingontheblockofmassMtopullit.Findtheforceoftheblockofmassm.

(a) ( )MF

m M + (b)mFM

(c)( )M m F

m +

(d) ( )mF

m M +

(2007)

27. Abodyofmassm=3.513kgismovingalongthexaxiswithaspeedof5.00ms1.Themagnitudeofitsmomentumisrecordedas(a) 17.57kgms1 (b) 17.6kgms1

(c) 17.565kgms1 (d) 17.56kgms1.(2008)

Answer Key

1. (b) 2. (c) 3. (a) 4. (b) 5. (b) 6. (b)

7. (d) 8. (a) 9. (d) 10. (c) 11. (d) 12. (a)

13. (a) 14. (d) 15. (a) 16. (a) 17. (b) 18. (c)

19. (a) 20. (b) 21. (b) 22. (b) 23. (d) 24. (d)

25. (d) 26. (d) 27. (a)

ma

mgsina

a

macosa

JEE MAIN 12


1. (b) : For no skidding along curved track,

v Rg = m

\ m0.6 150 10 30 .sv = =

2. (c) : Forobserver in the lift,acceleration=(ga)For observer standingoutside, acceleration = g.

3. (a) :F2 andF3 have a resultantequivalent toF1

\ Acceleration 1Fm

= .

4. (b) : T 60g = 60aor 960 (60 10)= 60aor 60a = 360or a = 6ms2.

5. (b) :1 2

1 2

( )( )m ma

g m m -

= +

\ 1 21 2

( )18 ( )

m mm m

- =

+

or 12

9.7

mm

=

6. (b) : Q Force= mass acceleration \ F TAB = ma

and TAB TBC = ma \ TBC = F 2 maor TBC = 10.2 (2 2 0.6)or TBC = 7.8N.

7. (d):Bytriangleofforces,theparticlewillbeinequilibriumunderthethreeforces.Obviouslytheresultant force on the particle will be zero.Consequently the acceleration will be zero.Hencetheparticlevelocityremainsunchangedat

.vr

8. (a) :When lift is standing,W1 = mgWhen the lift descends with acceleration a,W2 =m(g a)

\ 21

( ) 9.8 5 4.89.8 9.8

W m g aW mg

- - = = =

or2 1

4.8 49 4.8 24 N.9.8 9.8

W W = = =

9. (d):Weightoftheblock isbalancedbyforceoffriction \Weight of theblock = mR = 0.2 10=2N.

10. (c):Frictionalforceprovidestheretardingforce \ mmg = ma

or/ 6 /10 0.06

10a u tg g

m = = = = .

11. (d) : Acceleration of blockForce applied

( )Total mass

a =

or ( )Pa

M m =

+ \ Force on block

=Mass of block a ( )MP

M m =

+ .

12. (a) : Both the scales readM kg each.

13. (a): Initialthrust=(Liftoffmass)acceleration= (3.5 104) (10) = 3.5 105 N.

14. (d) : Suppose he can fire n bullets per second \ Force=Changeinmomentumpersecond

40144 (1200)1000

n =

or144 100040 1200

n =

or n = 3.

15. (a) : 1 21 2

( ) (5 4.8) 0.2( ) (5 4.8) 9.8m ma

g m m - -

= = = + +

or 20.2 9.8 0.2 0.2 ms .9.8 9.8

a g - = = =

16. (a) : For equilibrium of block,

q

fR

mgsinq

mgcosqmg

q

f =mgsinq \ 10= m 10 sin30or m = 2 kg.

17. (b) : Centripetal force on particle = mRw2

JEE MAIN 13

15PH YSI CS

\2

1 1 12

2 22

F mR RF RmR

w = =

w .

18. (c) : Component of g down the plane = gsinq \ For smooth plane,

21( sin )2

d g t = q ........ (i)

For rough plane,Frictional retardation up the plane= mk (gcosq)

gsinq

R

gcosqg

m qkgcos

q q

\ 21( sin cos )( )2 kd g g nt = q - m q

\ 2 2 21 1( sin ) ( sin cos )2 2 kg t g g n t q = q-m q

or sinq = n2 (sinq mkcosq)Putting q = 45or sin45 = n2 (sin45 mkcos45)

or21 (1 )

2 2 kn = - m

or 211 .kn

m = -

19. (a):Forupperhalfsmoothincline,componentofg down the incline = gsinf

\ v2 = 2(gsinf)2l

gsin fgcosf

g

m fk cosg

f f

R

Forlowerhalfroughincline,frictionalretardation= mkgcosf \ Resultant acceleration=gsinf mkgcosf

\ 0 = v2 + 2 (gsinf mkgcosf)2l

or 0 =2(gsinf)2l + 2g(sinf mkcosf)2

l

or 0 = sinf + sinf mkcosfor mkcosf = 2sinfor mk= 2tanf.

20. (b): Forfirstpartofpenetration,byequationofmotion,

22( ) 2 (3)

2u u f = -

or 3u2 = 24 f .... (i)For latter part of penetration,

2

0 22u fx = -

or u2 =8fx ......... (ii)From (i) and (ii)3 (8 fx)=24 f

or x = 1 cm.

21. (b) :F = kx

or 2015 3 N100

F = - = -

Initialaccelerationisovercomebyretardingforce.or m (acceleration a)= 3

or 23 3 10 ms .

0.3a

m - = = =

22. (b) : The incline is given an acceleration a.Accelerationof theblock is to the right.Pseudoacceleration a acts on block to the left. Equateresolved parts of a and g along incline. \ macosa = mgsinaor a = gtana.

23. (d) : Retardation due to friction = mgQ v2 = u2 +2as \ 0= (100)2 2(mg)sor 2 mgs = 100 100

or100 100 1000 m2 0.5 10

s = = .

24. (d) : Force time = Impulse = Change ofmomentum

\Impulse 3Force = 30 N.time 0.1

= =

25. (d) :Work done by hand = Potential energyof the ball

\ 0.2 10 2 20 N.0.2mgh

FS mgh Fs

= = = =

JEE MAIN 14


26. (d):Accelerationof thesystem Fa m M = +

Forceonblockofmass mFm mam M

= = +

.

27. (a):Momentumismv.

m=3.513kgv=5.00m/s \ mv=17.57ms 1Becausethevalueswillbeaccurateuptoseconddecimelplaceonly, 17.565=17.57.

JEE MAIN 15

17PH YSI CS

1. Aballwhose kinetic energy isE, is projected atanangleof45 tothehorizontal.Thekineticenergyoftheballatthehighestpointofitsflightwillbe(a) E (b) / 2 E (c) E/2 (d) zero.

(2002)

2. Ifmassenergy equivalence istaken intoaccount,whenwateriscooledtoformice,themassofwatershould(a) increase (b) remainunchanged(c) decrease(d) first increase then decrease.

(2002)

3. Aspringofforceconstant800N/mhasanextensionof5cm.Theworkdoneinextendingitfrom5cmto 15 cm is(a) 16J (b) 8 J(c) 32J (d) 24 J.

(2002)

4. Consider the following two statements.A. Linearmomentumof asystemofparticles is

zero.B. Kineticenergyofasystemofparticlesiszero.Then(a) Adoes not implyB andB does not implyA(b) A implies B but B does not implyA(c) Adoes not implyB but B implies A(d) Aimplies B and B implies A.

(2003)

5. Abodyismovedalongastraightlinebyamachinedelivering a constantpower.Thedistancemovedby the body in time t is proportional to(a) t3/4 (b) t3/2

(c) t1/4 (d) t1/2.(2003)

5 CHAPTER

Work, Energy and Power6. Aspringofspringconstant5103N/misstretched

initially by 5 cm from the unstretched position.Then the work required to stretch it further byanother 5 cm is(a) 12.50Nm (b) 18.75Nm(c) 25.00Nm (d) 6.25Nm.

(2003)

7. Aparticlemovesinastraightlinewithretardationproportionaltoitsdisplacement.Itslossofkineticenergy for any displacement x is proportional to(a) x2 (b) ex

(c) x (d) logex.(2004)

8. A particle is acted upon by a force of constantmagnitude which is always perpendicular to thevelocityof theparticle, themotionof theparticletakes place in a plane. It follows that(a) its velocity is constant(b) its acceleration is constant(c) its kinetic energy is constant(d) itmoves in a straight line.

(2004)

9. Auniformchainoflength2miskeptonatablesuchthatalengthof60cmhangsfreelyfromtheedge of the table.The totalmass of the chain is4kg.What istheworkdoneinpulling theentirechain on the table?(a) 7.2J (b) 3.6J(c) 120J (d) 1200 J.

(2004)

10. A force (5 3 2 )NF i j k = + + r

is applied over aparticlewhich displaces it from its origin to thepoint (2 )mr i j = -

r .Theworkdoneontheparticlein joule is

JEE MAIN 16


(a) 7 (b) +7(c) +10 (d) +13.

(2004)

11. Abodyofmassm,acceleratesuniformlyfromresttov1intime t1.Theinstantaneouspowerdeliveredto the body as a functionof time t is

(a) 11

mv tt

(b)2121

mv t

t

(c)2

1

1

mv tt

(d)21

1

mv tt

.

(2004)

12. Asphericalballofmass20kgisstationaryatthetopofahillofheight100m.Itrollsdownasmoothsurfacetotheground,thenclimbsupanotherhillofheight30mandfinallyrollsdowntoahorizontalbase at a height of 20 mabove the ground. Thevelocity attainedby the ball is(a) 10m/s (b) 34m/s (c) 40m/s (d) 20m/s

(2005)

13. The block ofmassMmovingon thef r i c t i on l e s sh o r i z o n t a lsurfacecollideswiththespringofspringconstantK and compresses it by length L.Themaximummomentum of the block after collision is

(a) zero (b)2ML

K

(c) MK L (d)2

2

KL

M(2005)

14. A mass mmoves with avelocityvandc o l l i d e sinelast icallywith anotheri d e n t i c a lmass. Aftercollision the firstmassmoveswith velocity in adirection perpendicular to the initial direction ofmotion.Findthespeedofthe2ndmassaftercollision

(a)2

3v (b)

3

v

(c) v (d) 3v(2005)

15. Abodyofmassmis accelerateduniformlyfromrest to a speed v in a time T.The instantaneouspowerdeliveredtothebodyasafunctionoftimeis given by

(a)2

2

1

2

mvt

T(b)

22

2

1

2

mvt

T

(c)2

2

mvt

T (d)

22

2

mvt

T

(2005)

16. AmassofM kgissuspendedbyaweightlessstring.Thehorizontal forcethatisrequiredtodisplaceituntil the stringmaking an angle of 45with theinitial vertical direction is

(a) ( 2 1)Mg - (b) ( 2 1)Mg +

(c) 2Mg (d) 2Mg

.

(2006)

17. Abombofmass 16kg at restexplodes into twopiecesofmassesof4kgand12kg.Thevelocityofthe12kgmassis4ms1.Thekineticenergyofthe othermass is(a) 96J (b) 144J(c) 288J (d) 192 J.

(2006)

18. A particle of mass 100 g is thrown verticallyupwardswithaspeedof5m/s.Theworkdonebythe force of gravity during the time the particlegoesup is(a) 0.5J (b) 0.5 J(c) 1.25 J (d) 1.25 J.

(2006)

19. Thepotentialenergyofa1kgparticlefreetomovealong thexaxis is given by

4 2( ) J

4 2x xV x

= -

.

The total mechanical energy of the particle 2 J.Then, themaximumspeed (inm/s) is(a) 2 (b) 3/ 2(c) 2 (d) 1/ 2.

(2006)

20. A 2kgblock slides on a horizontal floorwith a

M

aftercollision/ 3v

m

beforecollision

m

JEE MAIN 17

19PH YSI CS

speedof4m/s.It strikesauncompressedspring,andcompressesittilltheblockismotionless.Thekineticfrictionforceis15Nandspringconstantis10,000N/m.Thespringcompressesby(a) 8.5cm (b) 5.5cm(c) 2.5cm (d) 11.0cm

(2007)

21. Aparticleisprojectedat60tothehorizontalwithakineticenergyK.Thekineticenergyatthehighestpointis(a) K/2 (b) K (c) zero (d) K/4

(2007)

22. Anathleteintheolympicgamescoversadistance

Answer Key

1. (c) 2. (c) 3. (b) 4. (c) 5. (b) 6. (b)

7. (a) 8. (c) 9. (b) 10. (b) 11. (b) 12. (b)

13. (c) 14. (a) 15. (c) 16. (a) 17. (c) 18. (c)

19. (b) 20. (b) 21. (d) 22. (a) 23. (d)

of100min10s.Hiskineticenergycanbeestimatedtobein the range(a) 2,000J5,000J (b) 200J500J(c) 2105 J3105 J(d) 20,000J50,000J.

23. Ablockofmass0.50kgismovingwithaspeedof2.00ms1onasmoothsurface.Itstrikesanothermassof1.00kgandthen theymovetogetherasasinglebody.Theenergylossduringthecollisionis(a) 0.34J (b) 0.16J(c) 1.00J (d) 0.67J.

(2008)

JEE MAIN 18


1. (c):Kineticenergypointofprojection21( )

2E mu =

At highest point velocity = u cosq \ Kinetic energy at highest point

21 ( cos )2m u = q

2 21 cos 452mu =

.2E =

2. (c):Whenwateriscooledtoformice,itsthermalenergydecreases.Bymassenergyequivalent,massshould decrease.

3. (b) :2

1

0.15

0.05

x

x

W Fdx kx dx = =

\0.15 0.152

0.050.05

8008002

W xdx x = =

2 2400 (0.15) (0.05) = or W= 8 J.

4. (c) : A system of particles implies that one isdiscussing totalmomentum and total energy.

mmu

u

1( )a

1( )explodesa

1( )b

Totalmomentum = 0

But total kinetic energy = ( ) 212 2 muButiftotalkineticenergy=0,velocitiesarezero.HereA is true, but B is not true.A does not implyB, but B implies A.

5. (b) : Power =Work Forcedistance= = ForcevelocityTime Time

\ Force velocity = constant (K)or (ma) (at)= K

or1/ 2

Kamt

=

212

s at = Q

\1/2 1/ 2

2 3/ 21 12 2

K Ks t tmt m

= =

or s is proportional to t3/2.

6. (b) : Force constant of spring (k)= F/xor F= kx \ dW= kxdx

or0.1

2 2

0.05(0.1) (0.05)

2kdW kxdx = = -

[0.01 0.0025]2k = -

or Workdone

3(5 10 )(0.0075) 18.75 Nm

2

= = .

7. (a) : Given : Retardation displacement

ordv kxdt

=

ordv dx kxdx dt

=

or dv (v)= kx dx

or2

1 0

v x

vvdv k x dx =

or2 2 22 1

2 2 2v v kx - =

or2 2 22 1

2 2 2mv mv mkx - =

or2

2 1( ) 2mkK K x =

or Loss of kinetic energy is proportional to x2.

8. (c) : Nowork is donewhena forceof constantmagnitudealwaysactsatrightanglestothevelocityofaparticlewhenthemotionoftheparticletakesplace in a plane.Hence kinetic energy of the particle remainsconstant.

9. (b):Thecentreofmassofthehangingpartisat0.3m from table

JEE MAIN 19

21PH YSI CS

1.4m

0.6m

massof hangingpart 4 0.6 1.2 kg2

= = \ W = mgh= 1.210 0.3=3.6J.

10. (b) :Work done F r = r r

or work done (5 3 2 ) (2 )i j k i j = + + or workdone = 103 = 7 J.

11. (b) :Acceleration 11

va

t =

\ velocity (v) = 11

0v

at tt

+ =

\ Power P = Force velocity = mav

or2

1 1 12

1 1 1

v v t mv tP m

t t t = =

.

12. (b) :mgh =2

22

1 12

kmvR

+

=21 7

2 5mv

30m 20m

100m

2 71 802 5

mv mg \ =

or v2 =2 10 80 57 = 1600 57

or v = 34m/s.

13. (c) : Elastic energy stored in spring 212

KL =

\ kinetic energy of block 212

E KL =

Since p2 = 2ME

\222

2M KLp ME MK L = = = .

14. (a):Letv1=speedofsecondmassaftercollisionMomentum is conserved

Along Xaxis, mv1cosq = mv .......(i)

Along Yaxis,mv1sinq3

mv = ....... (ii)

From (i) and (ii)

\ (mv1cosq)2+(mv1sinq)2 =2

2( )3

mvmv +

or2 2

2 21

43

m vm v =

or 123

v v = .

15. (c) : Power = Force velocity=(ma) (v)= (ma) (at) = ma2t

or2 2

2Power ( )v mvm t t

T T = =

16. (a):Workdoneindisplacementisequaltogainin potential energy ofmass

Mg

F

l

lsin45

45lcos45

Work done sin452

FlF l = =

Gain in potential energy = Mg(l lcos45)

112

Mgl = -

\( 2 1)

2 2MglFl - =

or ( 2 1)F Mg = .

17. (c) : Linearmomentum is conserved \ 0= m1v1 + m2v2 = (12 4) + (4 v2)or 4v2 = 48 v2 = 12m/s

\ Kinetic energy ofmass 22 2 212

m m v =

21 4 (12) 288 J.2

= =

18. (c): Kineticenergyatprojectionpointisconvertedintopotential energyof theparticle duringrise.Potentialenergymeasurestheworkdoneagainstthe force of gravity during rise.

\ (workdone)=Kineticenergy= 212mv

JEE MAIN 20


or (work done)

( )21 100 5 55 1.25 J2 1000 2 10 = = =

\ Work done by force of gravity = 1.25.

19. (b):Total energyET = 2 J. It is fixed.Formaximumspeed,kineticenergyismaximumThepotentialenergyshouldthereforebeminimum.

4 2( )

4 2x xV x = - Q

or3

3 24 2 ( 1)4 2

dV x x x x x xdx

= - = - = -

For V to beminimum, 0dVdx

=

\ x(x2 1)=0, or x = 0, 1At x = 0, V(x)= 0

At x = 1, 1( ) J4

V x = -

\ (Kinetic energy)max = ET Vmin

or (Kinetic energy)max1 92 J4 4

= - =

or21 9

2 4mm v =

or2 9 2 9 2 9

4 1 4 2mv

m = = =

\3 m/s.2

mv =

20. (b):LetthespringbecompressedbyxInitialkineticenergyofthemass=potentialenergyof thespring+workdonedue tofriction

2 21 12 4 10000 152 2

x x = +

or 5000x2+15x16=0or x=0.055m=5.5cm.

21. (d):ThekineticenergyofaparticleisKAt highest point velocity has its horizontalcomponent.Thereforekineticenergyof aparticleathighestpointis

KH=Kcos2 q =Kcos260= .4K

22. (a): / 2v v = isaveragevelocitys=100m, t=10s. \ (v/2)=10m/s.vaverage=(v/2)=10m/s.

v

v/2

timet

v

Assuminganatheletehasabout50to100kg,his

kineticenergywouldhavebeen 21 .2 avmv

(1/2)mva 2v=(1/2)50100=2500J.For100kg, (1/2)100100=5000J.Itcouldbe in therange2000to5000J.

23. (d): By the lawofconservationofmomentummu=(M+m)v

0.502.00=(1+0.50)v,1.001.50

v =

InitialK.E.=(1/2)0.50(2.00) 2=1.00J.2

21 1.00 1.00Final K.E. 1.50 0.332 3.00(1.50)

= = =

\ Lossofenergy=1.000.33=0.67J.

JEE MAIN 21

PH YSI CS 23

1. Two identical particlesmove towards each otherwith velocity 2v and v respectively. The velocityof centre ofmass is(a) v (b) v/3 (c) v/2 (d) zero.

(2002)

2. Initialangularvelocityof a circulardisc ofmassM is w1.Then two small spheres ofmass m areattachedgentlytotwodiametricallyoppositepointson theedgeof thedisc.Whatisthefinalangularvelocity of the disc?

(a) ( ) 1M mM + w (b) ( ) 1M mm + w(c) ( ) 14MM m w + (d) ( ) 12MM m w + .

(2002)

3. A solid sphere, a hollow sphere and a ring arereleasedfromtopofaninclinedplane(frictionless)sothattheyslidedowntheplane.Thenmaximumacceleration down the plane is for (no rolling)(a) solid sphere (b) hollow sphere(c) ring (d) allsame.

(2002)

4. Momentofinertiaofacircularwireofmass M andradiusR about itsdiameter is(a) MR2/2 (b) MR2 (c) 2MR2 (d) MR2/4.

(2002)

5. A particle ofmassmmovesalong line PCwithvelocityvasshown.Whatis the angularmomentum ofthe particle about P ?

6 CHAPTER

Rotational Motion and Moment of Inertia

(a) mvL (b) mvl (c) mvr (d) zero.(2002)

6. AcirculardiscXofradiusRismadefromanironplate of thickness t, and another disc Yof radius4R is made from an iron plate of thickness t/4.Then the relation between themoment of inertiaIX and IY is(a) IY = 32IX (b) IY = 16IX(c) IY = IX (d) IY = 64IX.

(2003)

7. Aparticleperforminguniformcircularmotionhasangularmomentum L. If itsangular frequency isdoubledanditskineticenergyhalved,thenthenewangularmomentumis(a) L/4 (b) 2L (c) 4L (d) L/2.

(2003)

8. Let F r

be the force acting on a particle havingpositionvectorr

randT

rbethetorqueofthisforce

about the origin.Then

(a) 0and 0r T F T = r r r r

(b) 0and 0r T F T = r r r r

(c) 0and 0r T F T r r r r

(d) 0 and 0r T F T = = r r r r

(2003)

9. Asolidsphereisrotatinginfreespace.Iftheradiusofthesphereisincreasedkeepingmasssamewhichone of the following will not be affected?(a) moment of inertia(b) angularmomentum(c) angular velocity(d) rotational kinetic energy.

(2004)

O l

r

L

P

C

JEE MAIN 22


10. Onesolid sphereAand anotherhollow sphereBare of same mass and same outer radii. Theirmoment of inertia about their diameters arerespectivelyIA and IB such that(a) IA = IB (b) IA > IB(c) IA

PH YSI CS 25

19. A rounduniform bodyof radius R,massM andmomentofinertiaIrollsdown(withoutslipping)an inclined planemaking an angle q with thehorizontal.Thenitsacceleration is

(a) 2sin

1 /

g

MR I q

-(b) 2

sin

1 /

g

I MR q

+

(c) 2sin

1 /

g

MR I q

+(d) 2

sin

1 /

g

I MR q

-(2007)

20. Angularmomentumoftheparticlerotatingwithacentral forceisconstantdue to(a) constant torque(b) constant force(c) constantlinearmomentum(d) zero torque

(2007)

21. Forthegivenuniformsquarelamina ABCD,whosecentreisO,(a) 2AC EFI I =(b) 2 AC EFI I =(c) 3AD EFI I =(d) IAC= IEF

(2007)

22. Considerauniformsquareplateofside a andmassm.Themomentofinertia of this plateabout an

axisperpendiculartoitsplaneandpassingthroughoneof itscorners is

(a)22

3ma (b) 2

56

ma

(c)21

12ma (d) 2

712

ma

(2008)

23. A thinrodof length L is lying along the xaxiswithitsendsatx=0andx=L.Itslineardensity(mass/length)varieswith x ask(x/L)nwhere n canbezerooranypositivenumber.IfthepositionxCMofthecentreofmassoftherodisplottedagainstn,whichofthefollowinggraphsbestapproximatesthe dependence ofxCM on n?

(a)

xCM

On

LL2 (b)

O

L

L2

xCM

(c)

O

xCM

L2 (d)

O

L

xCM

L2

(2008)

D

AE

B

FC

O

Answer Key

1. (c) 2. (c) 3. (d) 4. (a) 5. (d) 6. (d)

7. (a) 8. (d) 9. (b) 10. (c) 11. (b) 12. (d)

13. (a) 14. (d) 15. (d) 16. (a) 17. (d) 18.

19. (b) 20. (d) 21. (d) 22. (a) 23. (b)

JEE MAIN 24


1. (c) :1 1 2 2

1 2c

m v m vv

m m +

= +

or(2 ) ( )

.2c

m v m v vvm m

+ - = =

+

2. (c):Angularmomentumofthesystemisconserved

\ 2 2 211 122 2

MR mR MR w = w + w

or Mw1 = (4m + M)w

or 1 .4M

M m w

w = +

3. (d):Thebodiesslidealonginclinedplane.Theydonotroll.Accelerationforeachbodydowntheplane = gsinq. It is the same for eachbody.

4. (a) :A circularwire behaves like a ring

M.I.about its diameter2.

2MR =

5. (d) : The particle moves with linear velocity valong linePC.The lineofmotion is throughP.Hence angular momentum is zero.

6. (d):Massofdisc 2( )X R t = p swhere s=density

\2 22 4( )

2 2 2XR t RMR R tI

p s p s = = =

Similarly,2 2

2(Mass)(4 ) (4 ) 162 2 4Y

R R tI R p

= = s

or IY = 32pR4ts

\4

41 1

2 6432X

Y

I R tI R t

p s = = p s

\ IY = 64 IX.

7. (a) :Angularmomentum L = Iw

Rotational kinetic energy 21( )2

K I = w

\ 22 2 2L I KL

K I w = = =

w w w

or 1 1 22 2 1

2 2 4L KL K

w = = =

w

\ 12 4 4L LL = = .

8. (d) : T r F = r r r Q

\ ( ) 0r T r r F = = r r r r r

Also ( ) 0F T F r F = = r r r r r

.

9. (b) : Free space implies that no external torqueis operatingon the sphere. Internal changes areresponsibleforincreaseinradiusofsphere.Herethe law of conservation of angular momentumapplies to the system.

10. (c) : For solid sphere, 225A

I MR =

For hollow sphere, 223B

I MR =

\2

22 3 35 52

A

B

I MRI MR

= =

or IA

PH YSI CS 27

1 1 0

0 0

i j k

r F

F \ = -

-

r r

( ) ( ).iF j F F i j = - = +

16. (a) :Angularmomentum is conserved \ L1 = L2 \ mR2 w=(mR2+2MR2) w=R2(m+2M) w

or .2m

m M w w =

+

17. (d) : cos452lAO =

122lAO \ =

45

O

A

D C

B

axis

l /2

l

2

l

or2lAO =

I = ID + IB + IC or222 2

2 2ml lI m = +

2 22 4

2 2ml mlI = +

or2

26 3 .2mlI ml = =

18. (M+m)=M= p(2R)2 swhere s=massperunitaream= sR2 s,M=3pR2 s R

O m2R

MOx

2 23 0R x R RM

p s + p s =

Becausefor thefulldisc,thecentreofmass isatthecentreO.

3Rx = - = aR. 1| | 3

- \ a = .

The centre ofmass is at R/3 to the left on thediameteroftheoriginaldisc.

Thequestionshouldbe atadistance aRandnot a/R.

19. (b) :Accelerationof a uniformbody of radiusRandmassM andmomentof inertia I rolls down(without slipping) an inclined planemaking anangle qwiththehorizontalisgivenby

2

sin

1

ga

IMR

q =

+ .

20. (d):Centralforcespassesthroughaxisofrotationso torqueiszero.If no external torque is acting on a particle, theangularmomentumofaparticleisconstant.

21. (d):Byperpendicularaxestheorem,2 22 2 2( ) 2

12 12 12EFM a aa b aI M M + + = = =

2 2 2(2 ) (2 ).

12 12 3zM a M a MaI = + =

Byperpendicularaxes theorem,

2

2 6z

AC BD z ACI MaI I I I + = = =

Bythesametheorem2

2 6z

EFI MaI = =

\ IAC=IEF.

22. (a) : For a rectangular sheetmoment of inertiapassingthroughO,perpendicularto theplate is

2 20 12

a bI M + =

a

b O

forsquareplateitis2.

6Ma

2 2 22.

4 4 22a a a ar r = + = \ =

A B

CD

a/2

a/2r

\ IaboutBparalleltotheaxisthroughOis2 2 2

2 46 2 6o

Ma Ma MaI Md + = + =

223

I Ma =

23. (b): 0C.M

0

Ln

n

Ln

n

k x dx xL

xk x dxL

=

JEE MAIN 26


12

0C.M 1

0

( 1)2

Ln

n

L nn

x dxnLx

n Lx dx

+ +

+ + = =

+

C.M( 1)( 2)L n

xn

+ = +

Thevariationofthecentreofmasswithx isgivenby

2 2( 2)1 ( 1)

( 2) ( 2)

n ndx LLdn n n

+ - + = = + +

If the rodhas thesamedensityas at x = 0 i.e.,n =0,thereforeuniform,thecentreofmasswouldhavebeen at L/2.As the density increaseswithlength,thecentreofmassshiftstowardstheright.Therefore it canonlybe (b).

JEE MAIN 27

29PH YSI CS

1. If suddenly the gravitational forceof attractionbetweenEarthandasatellite revolvingarounditbecomes zero, then the satellitewill(a) continuetomoveinitsorbitwithsamevelocity(b) move tangentially to theoriginal orbit in the

samevelocity(c) becomestationaryinitsorbit(d) movetowardstheearth.

(2002)

2. Energyrequiredtomoveabodyofmassmfromanorbitof radius2R to3R is(a) GMm/12R2 (b) GMm/3R2

(c) GMm/8R (d) GMm/6R.(2002)

3. The kinetic energy needed to project a body ofmass m from the earth surface (radius R) toinfinity is(a) mgR/2 (b) 2mgR(c) mgR (d) mgR/4.

(2002)

4. Theescapevelocityofabodydependsuponmassas(a) m0 (b) m1 (c) m2 (d) m3.

(2002)

5. Thetimeperiodofasatelliteofearthis5hour.Iftheseparationbetweentheearthandthesatelliteisincreasedto4timesthepreviousvalue,thenewtime periodwillbecome(a) 10hour (b) 80hour(c) 40hour (d) 20hour.

(2003)

6. TwosphericalbodiesofmassM and5M andradiiRand2R respectivelyarereleased infreespacewithinitialseparationbetweentheircentresequal

7 CHAPTER

Gravitationto12R.Iftheyattracteachotherduetogravitationalforceonly,thenthedistancecoveredbythesmallerbody just before collision is(a) 2.5R (b) 4.5R (c) 7.5R (d) 1.5R.

(2003)

7. Theescapevelocityforabodyprojectedverticallyupwardsfromthesurfaceofearthis11km/s.Ifthebodyisprojectedatanangleof45withthevertical, theescape velocitywill be(a) 11 2 km/s (b) 22km/s(c) 11km/s (d) 11/ 2 m/s.

(2003)

8. AsatelliteofmassmrevolvesaroundtheearthofradiusRataheightxfromitssurface.Ifgistheaccelerationduetogravityonthesurfaceoftheearth, theorbitalspeedof thesatellite is

(a) gx (b)gR

R x -

(c)2gR

R x +(d)

1/ 22gRR x

+

.

(2004)

9. The time periodofan earth satellite in circularorbit is independent of(a) themassofthesatellite(b) radiusof itsorbit(c) boththemassandradiusoftheorbit(d) neitherthemassofthesatellitenortheradius

of its orbit.(2004)

10. If g istheaccelerationduetogravityontheearthssurface,thegaininthepotentialenergyofanobjectofmassmraisedfromthesurfaceoftheearthtoaheightequalto the radiusR of theearth is

JEE MAIN 28


(a) 2mgR (b) 12mgR

(c) 14mgR (d) mgR.

(2004)

11. Supposethegravitationalforcevariesinverselyasthenthpowerofdistance.Thenthetimeperiodof a planet in circular orbitof radius R aroundthesunwill beproportional to

(a) ( )1

2n

R +

(b) ( )1

2n

R -

(c) Rn (d) ( )2

2n

R -

.

(2004)

12. Thechangeinthevalueofgataheighthabovethesurfaceoftheearthisthesameasatadepthdbelowthesurfaceofearth.Whenbothdandharemuchsmaller than the radius ofearth, thenwhichof the following is correct?(a) d=2h (b) d=h(c) d=h/2 (d) d=3h/2

(2005)

13. Aparticleofmass10giskeptonthesurfaceofauniformsphereofmass100kgandradius10cm.Findtheworktobedoneagainstthegravitationalforcebetweenthemtotaketheparticlefarawayfromthe sphere.(youmay takeG=6.67 1011Nm2/kg2)(a) 6.67 109 J (b) 6.67 1010 J(c) 13.34 1010 J (d) 3.33 1010 J

(2005)

14. Averagedensity of the earth(a) isdirectly proportional to g(b) is inverselyproportional to g

(c) doesnot dependon g(d) is a complexfunctionof g

(2005)

15. Aplanetinadistantsolarsystemis10timesmoremassivethantheearthanditsradiusis10timessmaller.Given that the escapevelocity fromtheearth is 11kms1, the escape velocity fromthesurfaceoftheplanetwouldbe(a) 0.11kms1 (b) 1.1kms1

(c) 11kms1 (d) 110kms1

(2008)

16. Directions : The following question containsstatement1andstatement2.Ofthefourchoicesgiven,choosetheonethatbestdescribesthetwostatements.(a) Statement1istrue,statement2isfalse.(b) Statement1isfalse,statement2istrue.(c) Statement1 is true, statement2 is true

statement2 is a correct explanation forstatement1.

(d) Statement1 is true, statement2 is truestatement2isnotacorrectexplanationforstatement1.

Statement1:ForamassMkeptatthecentreofa cube of side a, the flux of gravitational fieldpassingthroughitssidesis4pGM.Statement2:Ifthedirectionofafieldduetoapointsource is radialand itsdependenceon thedistance rfromthesourceisgivenas1/r2,itsfluxthrough a closed surface depends only on thestrengthofthesourceenclosedbythesurfaceandnoton thesize orshape of the surface.

(2008)

Answer Key

1. (b) 2. (d) 3. (c) 4. (a) 5. (c) 6. (c)

7. (c) 8. (d) 9. (a) 10. (b) 11. (a) 12. (a)

13. (b) 14. (a) 15. (d) 16. (c)

JEE MAIN 29

31PH YSI CS

1. (b) : The centripetal and centrifugal forcesdisappear,thesatellitehasthetangentialvelocityand it willmove in a straight lineCompare Lorentzian force on charges in thecyclotron.

2. (d) : Energy = (P.E.)3R (P.E.)2R

3 2GmM GmM

R R = - - -

.6

GmMR

= +

3. (c):Escapevelocity 2ev gR = \ Kinetic energy

21 1 22 2emv m gR mgR = = = .

4. (a) : Escape velocity2

2 eGM

gRR

= =

Escapevelocitydoesnotdependonmassofbodywhich escapesor it dependson m0.

5. (c) :According toKepler's law 2 3T r

\2 3 3

1 1

2 2

1 14 64

T rT r

= = = or

1

2

18

TT

=

or T2 = 8T1 = 8 5= 40 hour.

6. (c):Letthespherescollideaftertimet,whenthesmallerspherecovereddistance x1andbiggerspherecovered distance x2.Thegravitationalforceactingbetweentwospheresdependsonthedistancewhichisavariablequantity.

Thegravitational force,2

5( )(12 )

GM MF xR x

= -

Accelerationofsmallerbody, 1 25( )

(12 )

G Ma xR x =

-

Accelerationofbiggerbody, 2 2( ) (12 )GMa xR x

= -

Fromequationofmotion,2

1 11 ( )2

x a x t = and 22 21 ( )2

x a x

23

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