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Modern's abc + of Biology has been written specially for students of XII under 10+2 system of education of CBSE and other Boards following NCERTpattern of Examination. Ever since the publication of the first edition, the book has been receiving the overwhelming response from teachers and taughtalike. Keeping in view the recent edition of the book has been re-written as per latest syllabus. The book has been supplemented with practice problemsand some interesting facts for competitive examinations at the end of each chapter.All the objective type questions and very short answer questions havebeen answered. Special attempt has been made to make the book useful for students preparing for competitive examinations for entrance to variousmedical Colleges. Superfluous details present the text material in most practical and original way.With all these exclusive features, the book is bound to be the first choice of students all over India for Board and various competitive examinations.

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so as to provide an insight and a proper grip over the topic, as one learns it. The article work in each chapter of a unit is coupled withwell graded and carefully selected for easy comprehension of the beginners. So that the students can prepare fortheAnnual Examinations in an independent manner, a large number of and have beenincorporated in the book with proper Answers/Hints. for self-practice have been categorised into various types,so as to enable the students to choose the appropriate formula with ease. Further, detailed Hints/Solutions have been provided to UnsolvedNumerical Problems. offers a special feature of the book. It contains real and

It is aimed to provide intensive understanding and deep insight of the subject to the students, so that they get the feel of thetype of questions asked in competitive examinations, such as I.I.T.

in each unit forms another special feature of the book and consists of three parts. of thecontents of a unit is for easy and handy reference of various physical laws, principles, terms and formulae in that unit and for its quick revision.

such as and have been provided with solutions byadopting a novel technique in the form of Armed with this technique, the students will be able to attack the otherwisebrainteasing and seemingly incomprehensible numerical problems with great ease. set in various competitiveexaminations, such as etc have been thoroughly covered in the book. For the sake of easypreparation, these questions have been categorised into and Multiple Choice Questions. The author is of the firmopinion that the learning is a continual and gradual process. With the Competitive Examination Files on different units at their disposal, thestudents would be able to master them steadily all through the academic year, while preparing for admission to professional courses.

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MODERN'SOF

ABOUT THE BOOK

ABOUT THE BOOK

ABOUT THE BOOK

PHYSICS

CHEMISTRY

MATHEMATICS

BIOLOGY

India'sIndia'sNo.No.11

MODERN'SOF +

MODERN'SOF +

MODERN'SOF +

1. Units, Measurements, Dimensions, Errors of Measurements 1/1 – 1/42

2. Description of Motion in One Dimension 2/1 – 2/43

3. Description of Motion in Two and Three Dimensions 3/1 – 3/48

4. (a) Laws of Motion 4/1 – 4/53

(b) Uniform Circular Motion 4/55 – 4/94

5. Work, Power, Energy and Collisions 5/1 – 5/49

6. Rotational Motion 6/1 – 6/64

7. Gravitation 7/1 – 7/33

8. Properties of Matter 8/1 – 8/45

9. Oscillations 9/1 – 9/41

10. Wave Motion 10/1 – 10/36

11. Heat and Thermodynamics 11/1 – 11/34

12. Transference of Heat 12/1 – 12/27

Unit Test Paper No. 1 UT 1/1 – UT 1/3

Unit Test Paper No. 2 UT 2/1 – UT 2/3

Unit Test Paper No. 3 UT 3/1 – UT 3/3

Unit Test Paper No. 4 UT 4/1 – UT 4/3

� IMPORTANT FORMULAE, FACTS AND TERMS

UNITS AND MEASUREMENTS1. What is Physics ? The word physics is based upon a Greek world ‘fusis’ which

means ‘nature’. Thus Physics is a natural science which deals with the study of basic lawsof nature and exploration of the natural phenomena. It deals with the physical quantitieswhich can be measured and expressed in numbers such as mass, length, time, speed,velocity, force, work, energy, momentum and moment etc. Physics deals with measurementsas small as 10–15 m, 10–30 kg and 10–22 s. It also deals with large measurements of theorder of 1026 m, 1055 kg and 1018s. It helps us to study and understand systematically thevarious natural phenomena by way of observations and experiments. It is impossible todevelop anything new in science and technology without the help of Physics.

2. Need for Measurements. The measurement helps us in analysing the quantitativeaspects of the phenomena occuring in the physical world. The physics is an exact sciencebecause it is based on measurements.

3. Fundamental Physical Quantities. Those physical quantities which do not dependupon any other quantity are called fundamental quantities e.g., mass, length and time etc.

4. Derived Physical Quantities. The physical quantities which can be derived fromfundamental quantities and depend on them are called Derived physical quantities e.g.,velocity, acceleration, force etc.

5. Unit. The internationally accepted (standard) amount in terms of which we measurea quantity is called unit. For example, metre as the unit of length.

It is either defined coventionally or on the basis of a mathematical relation.(i) The unit of a physical quantity is that fixed and definite quantity which is taken to

be our reference standard to measure it.(ii) The magnitude of a physical quantity is given by the product of unit (u) selected

to measure it and the number (n) of times, that unit is contained in the given quantity i.e.,n × u ≈ constant = Q.

or nu

∝ 1 or u

n∝ 1

i.e., bigger the unit smaller is its numerical value.

6. Classification of Units. The units of a physical quantity can be classified asfollows :

(i) Fundamental units. The units of length, mass and time were the firstconventionally chosen units and were named as fundamental units. In fact, earlier, thelength, mass and time were thought to be the fundamental physical quantities in terms ofwhich the units of all other physical quantities could be expressed.

(ii) Basic units. It was found that the units of some more physical quantities need tobe included in the list of fundamental units. At present, in addition to the length, mass andtime, we take electric current, temperature, luminous intensity and amount of substanceas the fundamental units. To differentiate them from the earlier nomenclature, they are oftencalled as the basic (instead of fundamental) quantities and their units are called basic units.

1/1

Key Point

(i) ‘n’ is also called the numericalvalue of the quantity Q.(ii) The numerical value is alwaysa REAL POSITIVE NUMBER.(iii) The numerical value isinversely proportional to the unitselected to express the quantity.(iv) The product of numericalvalue and the unit is called theMAGNITUDE of quantity.(v) The magnitude of the quantityis always POSITIVE.(vi) For quantity which has nounits such as strain, relativedensity etc., the magnitudeconsists of numerical value only.(vii) Bigger the unit smaller is thenumerical value and vice versa.

UNITS, MEASUREMENTS,DIMENSIONS, ERRORS

OF MEASUREMENTS1

1/2 MODERN’S abc OF OBJECTIVE PHYSICS

Key Point

Angle is a physical quantity whichhas units but no dimensions.

(iii) Supplementary units. Two more conventionally chosen units are required toexpress the units of some physical quantities in terms of the basic units. They are the unitsof plane angle and that of the solid angle. They are called supplementary units.

(iv) Derived units. The units of physical quantities other than the basic units are calledderived units. They are obtained from the mathematical relationship between the givenderived physical quantity and the units of above mentioned seven basic quantities.

e.g., –1LengthSpeed = = Length × (Time)

Time

–2

2

LengthAcceleration Length (Time)

(Time)= = ×

Certain derived units are named in honour of great scientist e.g., unit of work is joule ;unit of force is named as newton, unit of capacitance as farad and so on.

7. System of Units. The set of basic, supplementary and derived units of variousphysical quantities is called system of units. The most widely used system of units is knownas the International System of Units. It is based on seven basic units (metre, kilogram,second, ampere, kelvin, candela and mole) and two supplementary units : radian andsteradian. It is abbreviated as S.I. The fundamental units on this system are chosen accordingto the following characteristics :

(i) They are well defined (ii) They have suitable size (iii) They are easily reproducible(iv) They do not vary with time, temperature, place and pressure, etc. (v) They are easilyaccessible (vi) They are indestructible. (vii) They should be easily convertible.

8. S.I. Units (System International Units).S.I. (international system of units) is universalization of M.K.S. system of units. It

has seven basic and two supplementary units as detailed below :

S.No. Physical quantity Unit Sym. Sym. ofunit

1. Mass Kilogram M kg2. Length or

Displacement Metre L m3. Time Second T s4. Electric current Ampere A A5. Luminous intensity Candela I Cd6. Thermodynamic

temperature Kelvin K K7. Amount of substance Mole mol mol, mole8. Plane angle Radian θ rad.9. Solid angle Steradian ω Sr.

The above system is coherent and rational system. It is meteric system and its multiplesand submultiple can be expressed as power of 10.

9. Prefixes or Multiples and submultiples

Factor Name of Symbol Factor Prefix Symbolprefix

101 deca da 10–1 deci d102 hecto h 10–2 centi c103 kilo k 10–3 milli m106 mega M 10–6 micro μ109 giga G 10–9 nano n1012 tera T 10–12 pico p1015 peta P 10–15 femto f1018 exa E 10–18 atto a1021 zetta Z 10–21 zepto z1024 yotta Y 10–24 yocto y

Key Point

Do not use plural form for unitse.g. centimetres.

Key Point

No full stop is used after thesymbol.

Key Point

(i) It should be noted that correctabbreviation for ‘gram’ is ‘g’ andnot ‘gm’. and that for kilogram is‘kg’ not kgm. Also second isabbreviated as ‘s’ and not ‘sec’ andhour as ‘h’ and not as ‘hr’.(ii) No ‘s’ is added to indicate theplural symbol of unit e.g., centi-metre and centimetres both arewritten as ‘cm’ and not cm. and‘cms’. In fact the abbreviation forboth singular and plural is thesame.

Key Point

(i) Prefix for multiples and sub-multiples are used either with basicunits or with units having namessuch as newton, joule, farad etc.Only for mass they are used withgram to avoid double prefix whichis never used.(ii) Prefix and symbol formsCOMPOSITE unit i.e. km3 andnot k (m)3.

UNITS, MEASUREMENTS, DIMENSIONS, ERRORS OF MEASUREMENTS 1/3

10. Some Important Derived Units with their names.

S. No. Physical qunatity Name of the unit Symbol Relation with the basic units

1. Force newton ; dyne N ; dyn N = kg ms–2, dyn = g cm s–2

2. All forms of energy, work }jouleerg

Jerg

2 2

2 2J = kg m serg. g cm s

−

−

=

3. Power watt W W = kg m2 s–3

4. Pressure pascal Pa Pa = N m–2 = kg m–1 s–2

5. Electric charge coulomb C C = A s6. Electric potential volt V V = kg m2 s–3 A–1

7. Electric Resistance ohm Ω Ω = kg m2 s–3 A–2

8. Conductance siemens S S = kg–1 m–2 s3 A2

9. Capacitance farad F F = kg–1 m–2 s4 A4

10. Inductance henry H H = kg m2 s–2 A–2

11. Magnetic flux weber Wb Wb = kg m2 s–2 A–1

12. Magnetic flux density tesla T T = kg s–2 A–1

13. Frequency hertz Hz Hz = s–1

14. Wavelength angstrom Å Å = 10–10m15. Modulli of elasticity pascal pa pa = kg m–1 s–2 or Nm–2

16. Coefficient of viscosity poise p p = g cm–1 s–1

poiseuille pl pl = kg m–1 s–1

17. Temperature kelvincelsiusfahrenheitreaumur

⎫

⎪

⎬

⎪

⎭

K°C°F°R

1 C 1 K5

1 F K95

1°R K4

⎫

⎪° =

⎪⎪

⎬° =

⎪

⎪=

⎪⎭

18. Loudness }belldecibell

BBd

11 B B

10d =

19. Electric Current ampere A one of basic units

20. Reactanceand

Impedence

⎫⎪

⎬

⎪⎭

ohm Ω Ω = kg m2 s–3 A–2

21. Susceptanceand

admittance

⎫⎪

⎬

⎪⎭

siemens S S = kg–1 m–2 s3 A2

22. Radioactivity curierutherfordbecquerrel

⎫⎪

⎬

⎪⎭

CiRdBq

10

61Ci = 3 7 10 dis./s

1Rd = 10 dis./s1Bq = 1 dis./s

⋅ ×

23. Radioactiveradiationexposure

⎫⎪

⎬

⎪⎭

roentgen R –

24. Mass (of stars) Chandershekher limit CSL –25. E.M.F. gilbert Gb –

11. Other Systems of Units. Following are the commonly used other system of units :(i) C.G.S. System of Units. This system of units was set up in France. In this system

centimeter, gram and second are choosen as basic units of length, mass and time respectively.(ii) F.P.S. System. It is also known as British system of units. In this system foot,

pound and second are choosen as basic units of length, mass and time respectively.(iii) M.K.S. System. In this system metre, kilogram and second are choosen as basic

units of length, mass and time respectively.

Key Point

(a) Symbols of units afterscientists name have initial capitalletter e.g. N for the newton.(b) Units after scientists name arenot written with capital initialletter e.g. newton NOT Newton.(c) The abbreviation of the unitsnamed after the name of scientistis written with capital initial lettere.g. newton is abbreviated as N.

1/4 MODERN’S abc OF OBJECTIVE PHYSICS

12. Definitions Of S.I. or Basic Units.(I) Units of Length. SI unit of length is metre (m). One metre is equal to 1650763·73

wavelengths in vacuum of a radiation emitted due to transition between the levels of 2p10and 5d5 isotope of krypton which has mass number 86. The light emitted by Kr-86 for thistransition has wavelength 6507·8021 Å. The number of these wavelengths in 1 m can becounted by using an optical interferometer.

Some of smaller units are :(i) 1 fermi or femto metre = 10–15 m(ii) 1 Angstrom (Å) = 10–10 m(iii) 1 micron or 1 micro metre (μm) = 10–6 m(iv) 1 millimetre (1 mm) = 10–3 m(v) 1 centimetre (1 cm) = 10–2 m(vi) 1 decimetre (1 dm) = 10–1 mSome of bigger units are :(i) 1 astromomical unit = 1AU (average distance of the sun form the earth)

= 1.496 × 1011 m(ii) 1 light year = 1 ly = 9.46 × 1015 m (distance that light travel with velocity of

3 × 108 ms–1in 1 year)(iii) 1 parsec = 3.08 × 1016 m (parsec is the distance at which average radius of earth’s

orbit subtends an angle of 1 arc second).(iv) “Cubit” was taken as the units of length of the arm from elbow to the tip of the

middle finger of a normal man and was taken to be about 10–1 m.(II) Units of Mass. Mass of a body is defined as the quantity of matter that body

contains. Mass of a body does not change with pressure, temperature or location of thebody in space. SI units of mass are kilogram (kg). The kilogram is defined as the mass ofcylinder having height 3·7 cm and diameter 3·7 cm and made up of Platinum-Iridium alloykept at international Bureau of weights and measures at Sevres.

Smaller units of measurement of mass are : Some other units of mass are : (i) 1 gram = 10–3 kg (i) 1 kg = 103 g = 0.0685 slug(ii) 1 centigram = 10–5 kg or 10–2 g (ii) 1 g = 6.85 × 10–5 slug(iii) 1 milligram = 10–6 kg or 10–3 g (iii) 1 slug = 14.59 kg(iv) 1 microgram = 10–9 kg or 10–6 g (iv) 1 u = 1.661 × 10–27 kg

(v) 1 quintal = 102 kg(vi) 1 metric ton = 103 kg

(III) Units of Time. It is the duration of 9,192,631,770 periods of durationcorresponding to the transitions between two hyperfine levels of Cs-133 atom in groundstate.

A solar day is defined as time that elapses between two moons of two consecutivedays and the average solar day is the mean of the solar days in a complete one year and

the second is 1

86400th part of a average solar day.

(IV) Kelvin (K). It is defined as the 1

273 16⋅ of the thermodynamic temperature of

triple point of water.(V) Ampere (A). It is defined as the constant current that when flows between two

parallel infinite straight conductors of negligible area of cross-section held one metre apartin vacuum, produces a force of 2 × 10–7 N per metre of their length.

(VI) Luminous Intensity or Candela (Cd) : One candela is the luminousintensity, in a given direction, of a source that emits monocromatic radiation of frequency540 × 1012 hertz and has radiant intensity in that direction of 1/683 watt per steradian.

(VII) Mole. It is defined as the amount of substance containing the same number ofatoms, molecules or ions etc. as there are atoms in 0·012 kg of C-12 isotope.

(VIIII) Supplementary units and their definitions : In addition to the abovementioned seven basic units, two supplimentary units are also used in SI. They are asfollows :

(a) The unit of plane angle called the ‘radian’. It is the plane angle between the tworadii of a circle which cut off on the circumference, an arc equal to the length of the radius.

Key Point

Metre is also defined as the lengthof the path travelled by light invacuum in a time interval of

1th

299792456 of a second of

time.

Key Point

Light year is unit of length ordistance and not of time.

Key Point

Do not use A.U for angstromunit.

Key Point

Index of notation should be usedfor expressing derived units interms of basic units e.g.m.s–1

instead of m/s as the units ofspeed.

UNITS, MEASUREMENTS, DIMENSIONS, ERRORS OF MEASUREMENTS 1/5

Key Point

Length of arcPlane angle in radian =

radius(b) The unit of solid angle is called the ‘steradian’. It is the solid angle with its

apex at the centre of a sphere that cuts out an area on the surface of the sphere equal tothe area of the square whose sides are equal to the radius of the sphere.

Solid angle in steradian = 2( )

area cut out on the surface of sphere

radius

13. Some Special Types of Units.1. 1 X-Unit (X.U) = 10–11 cm = 10–13 m.2. 1 nanometre (nm) = 10–7 cm = 10–9 m3. 1 light year = Distance travelled by light in vacuum in one year = 9.46 × 1015 m ≈ 1016m.4. 1 parsec (Parallactic second) ≈ 3.08 × 1016 m = 3.26 light year5. 1 astronomical unit (A.U.) = 1.5 × 1011 m.6. 1 shake = 10–8 s.7. One torr = 1 mm of Hg pressure.8. One barn = 10–28 m2.9. 1 pascal (Pa) = 1 N m–2.

10. One mach number = 1

1

Speed of moving object greater than 332 ms1

Speed of sound at 0°C in air . . 332 mss

i e≥

−

−υ

=υ

11. One attometre = 10–18 m.12. One nanometre = 10–9 m.13. One atmosphere = 105 N/m2.14. One atomic mass-unit (1 a.m.u.) = 1·66 × 10–27 kg.

14. Dimensional Analysis. Basic units of mass, length and time are denoted by [M],[L] and [T] respectively.

(i) Dimensions of a Physical Quantity. Dimensions of a physical quantity are thepowers to which the basic units of mass, length and time are to be raised in order to obtain

its units. e.g. speed =distance

time

[L]

[T][M LT ]0 –1= =

∴ Dimensions of speed are (0, 1, –1).(ii) Dimensional formula. Dimensional formula of a physical quantity is an expression

which tells which of the basic units of mass, length and time enter into its derived unitsand with what powers. e.g. dimensional formula of momentum = [M L T–1].

(iii) Dimensional Equation. The equation obtained by equating a physical quantityto its dimensional formula is called dimensional equation.

e.g. Area, A = Length × Length A = [M0L2T0]

DIMENSIONAL FORMULAE OF SOME IMPORTANT PHYSICAL QUANTITIES AND THEIR SI UNITS

S.No. Physical quantity Relation with basic quantities Dimensional formula SI units

1. Area Length × Breadth [M0L2T0] m2

2. Volume Length × Breadth × Height [M0 L3 T0] m3

3. Density Mass/VolumeM

L[ML T ]

3–3 0= km m–3

4. Relative or specific DensityDensity of substance

Density of water at 4 C°ML T

ML T[M L T ]

–3 0

–3 00 0 0= No units

5. Speed or velocity v = Distance

timeL

T[M LT ]0 1= − ms–1

Key Point

1 parsec > 1 Light year > 1 A.U

Key Point

1 Pa = 1 N m–2

= 10 dyne cm–2

Key Point

The word ‘second’ in case of‘parallactic second’ refers to theangular measurement and notsecond of time

Key Point

The measure of a physical quantityis independent of system of units.

Mach number is purely a numberand has no units or any dimensions.It is simply a multiplier e.g. a bodyis morning with 20 times thespeed of souand at 0°C in air i.e.332 ms–1

1/6 MODERN’S abc OF OBJECTIVE PHYSICS

S.No. Physical quantity Relation with basic quantities Dimensional formula SI units

6. Velocity gradientVelocity

distanceLT

LM L T

–10 0 –1= s–1

7. Acceleration or a = Velocity

time

LT

T[M LT ]

–10 –2= ms–2

Acceleration due to gravity

8. Momentum p = mass × velocity M × LT–1 = [MLT–1] kg ms–1

9. Force F = mass × acceleration M × LT–2 = [MLT–2] kg ms–2 or newton

10. Work or Energy W = Force × distance MLT–2 × L = [ML2T–2] kg m2 s–2 or joule

11. Stress or PressureForceArea

p = MLT

L[ML T ]

2

2–1 –2

−= kg m–1 s–2 or

N/m2 or pascal

12. Impulse I = Force × time MLT–2 × T = [MLT–1] kg ms–1 or Ns

13. (a) Torque or Moment of force τ = Force × ⊥ distance MLT–2 × L = [ML2T–2] kg m2s–2 or Nm

(b) Torque τ = Iα ML2 T–2 kg m2 sec–2

(c) Angular Impulse τ t ML2 T–1 kg m2 sec–1

14. Gravitational constant GForce (distance)

mass mass

2=

××

MLT L

M M

2 2− ××

kg–1 m3s–2

= [M–1L3T–2] or Nm2/kg2

15. Surface tensionForce

TLength

= MLT

L[ML T ]

20 2

−−= kg s–2 or Nm–1

16. Spring constant or Force KRestoring force

displacement=

MLT

LML T

–20 2= − kg s–2 or Nm–1

constant

17. (a) Intensity of GravitationalForce

EMass

= MLT

M[M LT ]

20 2

−−= ms–2 or N/kg

field

(b) Gravitational potential = Work

MassM°L2 T–2 m2 sec–2

(c) Gravitational potential ML2 T–2 joule

energy = – GMm

r

18. Coefficient of Viscosity η =×

Force

area velocity gradientMLT

L T[ML T ]

2

2 11 1

−

−− −

×= kg m–1s–1 or Nm–2s

or Deca poise.

19. Coefficient of Restitution = R.V. of separation

R.V. of approachM°L°T° No units

20. PowerWork

PTime

= ML T

T[ML T ]

2 22 3

−−= kg m2 s–2 or watt

21. StrainChange in dimensions

Original dimensionDimensionless —

22. Modulus or coefficientStress

Strain

–1 –21 2ML T

[ML T ]M°L°T°

− −

=kg m–1 s–2 or N/m2

of elasticity

Moderns ABC Of Objective Physics JEEMain Part-1

Publisher : MBD GroupPublishers

ISBN : 9789383907588Author : R. P. Arora, O. P.Kakkar, Deepak Chopra,Sameer Arora

Type the URL : http://www.kopykitab.com/product/11993

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