Mechanics for JEE (Main & Advanced) Volume 1

565 Pages·2014·19.72 MB·English

by  Er. Anurag Mishra

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·' !II Published by: 't§l
SHRI BALAJI PUBLICATIONS
(EDUCATIONAL PUBLISHERS & DISTRIBUTORS)
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Jansath Road, Muzaffarnagar (U.P.)
Phone: [phone] (0), 2600503 (R)
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!II First edition 2009
!II Fourth edition 2012
!II Fifth edition 2013
!II Reprint 2014
!II © All rights reserved with author
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, · Preface
I have been involved in teaching Physics for last 16 years. This book is an opportunity to
present my experiences. During my interaction with UT-JEE aspirants. I realised that most
feared topic is mechanics. Some oft he reasons put forward by students behind this thought
were:
@ No spontaneous thoughts.appear after reading a problem. Mind goes blank. Can not
. proceed in a problem.
@ How to ~roceed in a problem? Which law is applicable; that is a given problem will
involve conservation of energy or momentum or both.
@ If some one says solve the problem in non-inertial reference frame, horrible thoughts
appear inmind.
@ Total confusion about CM frame.
@ Proper understanding of constraints.
@ S)lort cut approach in relative motion.
@ No single book available that gives large no. of solved examples with elaboration of
concepts in asolµtion.
This book will help the students in building analytical and quantitative skills,
addressing keyl,Jlisconceptions and developing.confidence in problem solving.
I sincerely wish that this book will fulfill all the aspirations of the readers. Although
utmost full care has been taken to make the book free from error but some errors
. - . .
ina_dvertently may creep-in. Author and Publisher shall be highly obliged if suggestions.
regarding improvement and errors are pointed out by readers. I am indebted Neeraj Ji for
providing me an opportunity to write a book oft his magnitude.
I am indebted to my father Sh. Bhavesh Mishra; my mother Smt. Priyamvada Mishra, my
wife Manjari, my sister Parul, my little kids Vrishank and Ira for giving their valuable time
which I utilized during the writing of this book and people of Morada bad, who supported
. .
·me throughout my career.
In the last, !also pay my sincere thanks to all the esteemed members ofM/s. ShriBalaji
Publications in bringingo ut this book in"the present form.
Anurag Mishra.
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Our Other Publications
for
(Engineering Entrance Examination)€
Er. Anurag Mishra Er. Anurag Mishra • Electrostatics
Mechanics • Simple Harmonic Motion Electricity& , •, Electric Current
j •
!•JEE • Wave Motion Magnetism yapacitors
• Solid and Fluids forJEE lI • The Magnetic Field
'
• Gravitation 1 • Electromagnetic Induction
Vol. II
/ and A.G. Circuits
'I-----~
Er. Anurag Mishra I' .
)feat&
1 • Temperature, Heat & Optics .
Thermodynamics
tl)e. equation of State. l "G eometrical Optics'
/•JEE Heat Transfer . foJ EE
Wave Opti~
• Thermodynamics
. I ,
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How to face the challenge ?
Following are some doubts which arise in the mind of almost all the students
but may face them by taking some care.
1. I can not solve numerical because my concepts are not clear. In fact numerical
solvingitselfis an exercise t~ learn concepts.
·z.
1 can not study because I am in depression, I fell into it because I was not
/'
studying! Depression is escape mechanism of people afraid of facing failures.
Failure is integral partoflearning.
3. I understand everything in class but can not solve on my own.WRITING work is
· vital. It is a multiple activity, initially idea comes in mind then we put into
language to express it, we are focussed in hand eye coordination, eyes create
visual impression on brain which isrecorded there. WRITING WORKS ARE
EMBOSSED ON BRAIN LIKE CARVINGS OF AJANTACAVES.
4. In exams my brain goes blank, but I can crack them at home. Home attempt is
your second attempt! you are contemplating about it while home back. You
do not behave differently in exam you replicate your instincts. Once a fast
bowler was bowling no balls. His coach placed a-stump on crease, in fear of
injury he got it right. CONCEPTUALIZATION, WRITING EQUATION, SOLVING,
THEN PROBLEM GETS TO CONCLUSION!
5. I am an average student. It is a rationalization used by people afraid of hard
work. In their reference frame Newton's first law applies "if I have a
misconception I will continue with it unless pushed by an external agent
even I will surround him in my web of misconception yielding zero
resultant:' AVERAGE IS NOT DUE TO CAPACITY LACUANEBUT DUE TO LACK
OF DETERMINATION TO SHED INERTNESS.
6. A famous cliche "/ do not have luck in my favour' PRINCIPLE OF CAUSALITY:
CAUSE OF AN EVENT OCCURS IN TIME BEFORE OCCURRENCE OF THAT
EVENT i.e., cause occurs first then event occurs. SHINING OF LUCK IS NOT AN
iNSTANTANEOUS EVENT IT IS PRECEDED BY RELENTLESS HARD WORK.
Sow a seed ofaspiration in mind, water it with passion, dedication it will bear
fruit, luckcan give you sweeter fruit.
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t. Do not take study as a burden actually )ts a skill like singing and dancing. It
has to be honed by proper devotion and dedication. ·
2. Withou't strong sen_se of achievement you can't excel. Before entering the
cmppeti.tive field strong counselling by parents is must. Majority do not
· know what for they are here. No strategic planning, they behave like a tail
: ende_r batting in frontofSteyn's bouncers.
3. - 'science is not a subje,ct based on well laid dowh procedures or· based on
it
learning sonie facts, ipvolves very intuitive and exploratory approach.
Unless their is desire and passion to learn you can not discover new ideas. It
requires p'atience and hard work, whose fruits may be tangible later on.
4. Some students realize very late that they are studying for acquiring skills and
, . honingthem. Their is a feeling that they can ride at the back of instructor and
,
· , achieve ~xcellence. Study comes as tqrtu·rous exercise enforced on them and
'
their is some mechanism that can take this burden-of them. -
5. Science is not about gaining good marks, up toXth by reading key points good
marks are achieved but beyond that only those survive who have genuine
interest in learning and exp to ring. Self study habit is must.
6. · IF YOU WANT TO GAIN LEAD START EARLY. Majority of successful students
try to finish .major portion-elementary part of syllabus before they enter
Coaching Institute. Due to this their maturity level as comparecl to others is
· more tliey get ample time to adj4st with th~ fast pace. They are less·
' :i.
traumatized by the scientific matter handed over. For those who enter fresh
must be counselled to not get bullied by ·early starters but work harder
initially within first two months initial edge is neutralized.·
7. Once a sl:l,ldent lags behind due to scime forced or unforced errors his mind
begins to play rationalization remarks like I am an average student, my mind
is not sharp enough, I have low IQ etc: These words are mechanisms _used to
· a\Toid hard work. These words a,re relative terms a person who has .early start
may be intelligentr~lative t9y6u.' . . .
0lntelligence means _cu~ulative i-~sult of h_ard _work of previous years, that
hard work has eventuallY. led to a developm~nt of instinct tci crack 'things -
easily. _., ·
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I '
CONTENTS
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UNIT AND DIMENSIONS
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I. DESCRIPTION OF MOTION
I -
Subject of kinematics (19), Vector notation (20), Displacement
vector (20),Parallelogram law of vector addition (21).,
Component ofvector(23), Unitvector(24), Expressing a vector
in unit vector notati_on (25), Position vector (27), Rectangular
resolution of a vector in three dimensions (28), Vector
multiplication (31), The scalar product of two vectors (32),
The vector product of two vectors (35), Rectilinear motion of
a particle (37), Calculus supplementary ( 41), Rectilinear
motion ( 44), Instantaneous velocity ( 45), Integration ( 48),
Interpretation of graphs (53), Average velocity & Average
speed (58), Two-dimensional motion with constant acceleration (69), Projection on an inclined plane
(82), Relative motion (87), Application of advanced concept of relative motion (88), Equation of
motion for relative motion (98), Projection of a particle in an accelerated elevator (101), Projection of
a ball in horizontally moving trolley (101 ), Closest distance of approach between two moving bodies
(102), Problems: Level-1 (106), Level-2(113), Level-3 (117),Answers(123), Solutions (124).
Q
2. FORCE ANALYSIS
~~~~~p=--=~-=::;~
The concept of force (138), Reference frame (139), Ideal string
(143), ideal pulley (143), Contact force (143), Concept of
external and internal force (144), Pulley system (145), Tension
in a hanging rope (145), Constrained motion (148), Pulley
constraint (154), Normal constraint (155), Elastic force of
spring (158), Parallel combination (159), Friction (165), The
laws of sliding friction (165), Direction of kinetic Friction
(171), FBD when arm is in_ deceleration (185), Circular
motion (186), Angular velodty vector (187), Concept of ,
pseudo force (192), Non-inertial reference frame (193),
Whirling rope (195), Lift Force on an airplane (196 ), Non-uniform circular motion on horizontal plane I
{196), Problems: Level-1 (210), Level-2 (221),Level-3 (230),Answers (238), Solutions (240).
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3. WORK AND ENERGY
Work done (265), Unit of work (266 ), Conservative and non-conservative
force (268), Concept of potential energy (269), Classical work energy theorem
(270), Conservation of mechanical energy (271), Work done by friction
(271), Work done by spring force (271), Work depends on the frame of
reference (272), Work due to internal force (friction) (272); Work energy
theorem in a non-inertial reference frame (273), How to apply
coriservation of energy_ equation (273), Vertical circ_ular motion (283),
Power (293), lntemai energy so!-lrces & work (296), Problems Level-1
(299), Level-2 (306), Level-3 (310),Answers (316), Solutions (318).
CJ
4. IMPULSE AND MOMENTUM
Impulse (328), Conservation of momentum (328), Conservation
momentum for a two particle system (329), Relative velocity and the
conservation of momentum (330), Recoil disintegration, explosions (335),
Impulsive force (336 ), Centripetal acceleration revisite~ (338), Centre of
mass (340), Position of COM oft wo particles (340), Centre of gravity (341 ),
Motion of the centre of mass (34,1), Kinetic energy of a system of particles
(342), Most important concept (343), Finding the centre of mass by
integration (353), Collisions (361), Models for elastic & inelastic
collisions (362), Oblique impact (365), The velocity of the centre of
mass for collisions (370), Elastic collisions in the CM reference frame (371), Inelastic collisions in CM
reference frame (372), System of variable mass; Rocket propulsion (380), Problems Level-1 (383),
Level-2 (395), Level-3 (399), Answers (4 06), Solutions (4 08). ·
(J
5. RIGID BODY MOTION
What is rigid body(4 21), General rigid body motion (4 21 ), Rotation about centre
of mass (4 22), Kinematics of fixed axis rotation (4 22), Vector representation of
rotational quantities (4 25), .Torque (4 27), Newton's second law for rotation
(4 29), Rotational kinetic energy and moment of inertia (4 30), Rotational
kinetic energy of a collection of particles (431), Perpendicular axis theorem
(4 37), Dynamics of a rigid body(4 41), Angular momentum (4 47), The ladder
(450), Work done due to torque (457), Angular momentum of a projectile
,,
(4 62), Angular momentum of an i[]verted conical pendulum (4 62), Angular '=--~='-~=-~=~--
impulse angular momentum theorem (4 64), Two bodies rotatory system
0
(4 66), Kinematics ofrigidbody rotation (4 75), Total kinetic energy of body (4 84), Dynamics of rigid body in
plane motion (486), Torque on the rotating skew rod (506), Problem: Level-1 (511); Level-2 (519), Level,3
(525), Answers (531), Solutions (533), Exercisg_,_advanced problems (544), Comprehension based
pro bl ems ( 553), Assertion and reason type problems (562). I
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UNIT AND DIMENSIONS .
Physics is that branch of science in which we observe, (a) Magnitude of Physical Quantity=
measure and describe natural phenomena related to matter Numerical value x Unit
and energy. Like all the science, physics is ultimately based
th us for a given physical quantity when the unit will
on observation. To ~ssemble the relevant observations into a
change, numerical value will also change, e.g. density of
coherent picture by, constructing a logical framework is water =lg- cc-1 = 103kg- m-3and not lkg- m-3.
called theory. Theory enables the physicist to account for
(b) Larger the unit smaller will be the magnitude and
past observations and to decide how new ones should be
vice-versa, e.g., 1 kg= 1000 gm then as 1000 is greater than
made. Nearly all physical observation are quantitative; they
1, gm is smaller unit than kg of mass.
require measurement.
Every measurement is a comparison of a Criteria for Standards
quantity with a standard quantity that is, an The choice of the standard is arbitrary. However, several
agreed upon quantity of the same kind. To measure a criteria must be met if a standard is to be as useful as
length for example, you adopt as your standard a convenient possible.
measuring rod, whose length you use as the unit of length. 1. Stability : The standard should not vary with time.
You count the number of times that the rod fits into the If this criterion is satisfied, measurements made at different
length to be measured. This number given the length in time, using the same standard, can be meaningfully
terms of the chosen unit. compared.
Physical Quantities 2. Reproducibility: The standard should be accurately
The quantities by means of which describe the laws of reproducible so that copies, ideally identical with the
physics are called Physical Quantities. A physical quantity is standard itself can be used elsewhere. If this criterion is
complete specified if it has - satisfied, measurements made at different places can be
~---e>(A) Numerical value only ratio e.g., compared.
refractive index, dielectric constant, etc.
3. Acceptability : The standard should be universally
or
accepted so as to eliminate clumsy and possibly inaccurate
Magnitude only Scalar e.g., comparisons among measurement made with separate
mass, charge,current etc.
standard.
or
4. Accessibility : As nearly as possible, the standard
should be readily accessible to everyone ·vho needs to use it.
Magnitude and direction Vector e.g.,
displacement, torque, etc. 5. Precision : It should be possible to measure the
In expressing the magnitude of a physical quantity we standard itself with a precision at least as great as the
choose a unit and then find physical quantity how many times precision with which any comparable measurement can be
that unit is contained in the given physical quantity, i.e. made.
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