-
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.
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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.
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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
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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
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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
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4 C h a p t e r w i s e A I E E E E X P L O R E R
(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
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6 C h a p t e r w i s e A I E E E E X P L O R E R
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
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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
-
12 C h a p t e r w i s e A I E E E E X P L O R E R
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
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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
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14 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. (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
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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
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16 C h a p t e r w i s e A I E E E E X P L O R E R
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
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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
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18 C h a p t e r w i s e A I E E E E X P L O R E R
(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
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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
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20 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. (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
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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
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22 C h a p t e r w i s e A I E E E E X P L O R E R
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
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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
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24 C h a p t e r w i s eA I E E E E X P L O R E R
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
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26 C h a p t e r w i s eA I E E E E X P L O R E R
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
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28 C h a p t e r w i s eA I E E E E X P L O R E R
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
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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
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30 C h a p t e r w i s eA I E E E E X P L O R E R
(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
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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