PHYSICS BY Rajneesh Mutha(NWUPT IIT Kanpur,ALTOP IITK)(Member Indian Association of Physics teachers)Trained by Prof. H C Verma at IIT Kanpur

A briefing about our method We will follow HCV point to point The entire course is divided into 100 lectures You will get a booklet with every lecture A lecture booklet will contain the following1 Theory,definitions,intext examples2 One Sheet

There is a test every week At the end of a chapter we will discuss all questions of HCV NCERT,Bansal classes study material

A few words about JEE The syllabus consist of six branches1 Mechanics Chapter 1 to 14 HCV -30 to 35% questions are from this2 Waves - Chapter 15,16- 15%3 Heat and thermodynamics - Chapter 23-28 HCV-15 to 20%4 Optics-Ch 18-22 -10 to 15%5 Electricity and Magnetism Ch 29-40,30-35%6 Moden Physics- Ch 41-47 -20% In JEE 2012 Cut off was 10% Somebody who scores 50% got a rank somewhere around 2000

Chapter 2 Physics and MathematicsLEC 11 Vectors and scalarsA quantity which needs direction and magnitude both to express itself is called a vector examples are velocity,accerleration,force. We will represent a vector by a bold letter and magnitude by ordinary letter.Thus F is a vector and F is its magnitude.A quantity otherwise is called a scalar.A vector is represented by an arrow whose length tells the magnitude and whose direction is the direction of vector

2 Equality of vectorsIf two vectors are parallel and have same magnitude they are equal. That is a vector is glided parallel to itself.3 Addition of vectorsVectors are added by triangle law which isFor a+b glide a or b such that as head is in bs tail then vector joining as tail to bs head gives R= a+b.R called the resultant of a and b .

a+bb b aa Practicing tringle law in classIn the following find a+b, b+a

aa b a bab b a b aa bb

Formula and its derivation

Practicing formula in the class1 Two vectors of magnitude 3 and 4 unit acts at 90 find the resultant.2 Two vectors each of magnitude 5 N are acting at 120 find the resultant.3 Two vectors 5N and 12N has 13N as their resultant find angle between them.4 If two vectors of equal magnitude has there resultant equal to each of them find their resultant.5 If two vectors F and3/2 F act at 150 find the resultant.

Sheet1 If three vectors of equal magnitude act at 120 each find the resultant.2 What can be the maximum and minimum of resultant of two vectors.3 If two vectors each of magnitude F acts at angle find their resultant by formula and graphical method.5 Five sides of a pentagon represent five vectors taken in order. Show their resultant is zero.6 In a and b, as magnitude is greater show that resultant will be tilted more towards a.7 Can you divide a vector into two or three vectors using triangle law.8 If all the sides and diagonal of a square are considered vectors and added what is the resultant?9 If for a triangle three sides taken in order and any median are represented by vectors what is the relation between them LEC 2 VECTORS2.4 Multiplication of a scalar by a vectorSuppose there is a vector a if we multiply it by k its magnitude gets k times but its direction remains same. The negative of a vector is a vector obtained by rotating the original vector by 180.2.5 Subtraction of vectorsWe simply write a-b=a+(-b) Practicing vector subtraction in the class.In the example given in LEC 1 for each pair find a-b and b-a 2.6 Resolution of vectorsIt is simply dividing a vector into many vectors. Each of many vectors thus obtained are called components of the original vectors. If all the components lie in one plane the resolution is called two dimensional otherwise three dimensional

ax =a cos in the above figure is called the horizontal or x component of a where as ay=a sin is called y or vertical component. Find x and y components of the following vectors 5m 4m 3045 60 45

5m 5mUnit vectors,the i,j,k form A unit vector means a vector of magnitude 1.The unit vectors in the X,Y,Z directions are i,j,k.So a vector of magnitude 4 in X direction is 4i. It can also be written as a=ax i+ay jSheet 1 For the following six problems, draw the indicated vector and show the components into which it is resolved. Calculate (after estimating) all answers. 1. A person walks 200 meters at 27 degrees North of East2. A car moves 60 m/s at an angle of 35 degrees West of South3. A magnet attracts a steel ball with a force of 220 newtons at 25 North of West4. A rocket accelerates at 45 m/s at 65 degrees South of East5. A cannonball is launched with a speed of 170 m/s at 40 above the horizontal6. The momentum of an ocean liner is 3.75 x 10 N-s at 30 North of East7 2.5 m/s, 45 deg and 5.0 m/s, 270 deg and 5.0 m/s, 330 deg8 4.0 m/s, 90 deg and 2.0 m/s, 0 deg and 2.0 m/s, 210 deg9 2.0 m/s, 315 deg+ 5.0 m/s, 180 deg+ 2.0 m/s, 60 deg= 2.61m/s, 173 deg10 3.0 m/s, 45 deg and 5.0 m/s, 135 deg and 2.0 m/s, 60 deg11 2.0 m/s, 150 deg and 4.0 m/s, 225 deg12 8.0 m/s, 330 deg and 4.0 m/s, 45 deg

LEC 3System for finding resultant by vector resolution method1 Attatch a frame2 Mark angles3 Find components4 Find H and V5 Find R=H2+V2 tan=V/H here is angle of resultant with x axis.Classroom examplesFind the resultant in the following cases by vector resolution

5m 6m 10m 10m 45 60 30 5m 4m 10m

Sheet1 Repeat all the classroom examples 2 Find resultant by resolution in the following casesQ 7 to 12 of the previous sheet

LEC 42.6 Resolution of vectorsThe i,j,k form- The i,j,k form is

In this a=ax2 + bx2 + cx2Also if

And magnitude of resultant is

2.7 Dot product or scalar productThe dot product (also called scalar product) of two vectors a and b is defined as

(How)2.8 Cross product or vector product

Cross product of i,j,k

The i,j,k cycle

Class room practice of cross product

Sheet In the following pairs find AXB,A.B,A,B and angle between themi+2j+k,i-j 3i+2j-7k,i-2j+k 7i+7j+7k,i+j+k i-8j,7j+j i-2j+k,i+j+k.

LEC 52.9 DIFFERENTIAL CALCULUSThe meaning of function and algebrical presentation.The average rate of change and its calculation for some functions.The instantaneous rate of change and derivative-Calculation of derivatives for some simple functionsFormula of differentiation and its practice

Classroom examples

LEC 61 Graphical representation of functionsSome important graphs-linear function,quadraticFinding average rate of chane by graphFinding dy/dx by graph2 Integration Formulae

3 Practicing definite integration- Some classroom examples4 Integration in graphsf(x)dx a to b is area under f(x)-x curve from a to bSome classroom examplesSheet 11 Draw the graph of y=x2+7 and find average rate of change from x=2 to x=3.2 In above find dy/dx at x=2,3 by graph and by formula.3 In above graph integrate 2 to 3 also find this integral by formula.4 Repeat q 1 to 3 for function y=1/x.5 Repeat q1 t0 3 for y=2x-16 Repeat q1 to q3 for x=1/2 gt2Do the following integrations

LEC 72.12 Significant figuresRules- 1 Zeroes in the beginning are never significant.2 Zeroes are significant in the end only if they come after decimal.2.13 Significant figures in calculations1 In addition answer must contain minimum number of decimal places.2 In multiplication and division answer must contain minimum number of decimal places.3 Rules for rounding off.2.14 Average value,absolute error,mean absolute error.Types of errors In general, the errors in measurement can be broadly classified as (a) systematic errors and (b) random errors.Systematic errorsThe systematic errors are those errors that tend to be in one direction, either positive ornegative. Some of the sources of systematic errors are :(a) Instrumental errors that arise from the errors due to imperfect design or calibrationof the measuring instrument, zero error in the instrument, etc. For example, the temperature graduations of a thermometer may be inadequately calibrated (it may read104 C at the boiling point of water at STP whereas it should read 100 C); in a verniercallipers the zero mark of vernier scale may not coincide with the zero mark of the mainscale, or simply an ordinary metre scale may be worn off at one end.(b) Imperfection in experimental technique or procedureTo determine the temperature of a human body, a thermometer placed under the armpit will always give a temperature lower than the actual value of the body temperature. Other external conditions (such as changes in temperature, humidity, wind velocity, etc.) during the experiment may systematically affect themeasurement.(c)Personal errors that arise due to an individuals bias, lack of proper setting ofthe apparatus or individuals carelessness in taking observations without observingproper precautions, etc. For example, if you,by habit, always hold your head a bit too farto the right while reading the position of a needle on the scale, you will introduce anerror due to parallax. Systematic errors can be minimised by improving experimental techniques, selecting better instruments and removing personal bias as far as possible. For a given set-up, these errors may be estimated to a certain extent and the necessary corrections may be applied to the readings. The random errors are those errors, which occur irregularly and hence are random with respect to sign and size.Illustration of error,absolute error,mean absolute error by an example.Combination of errors Proofs will be given in the class1 In addition and subtraction errors are added.2 In multiplication and division relative errors are added.3 In dealing with powers before adding we must multiply them by their powers.Sheet 1 and Sheet 2All questions of HCVLEC 8Question for short answer and OB I HCVLEC 9OB II and Exercise HCVLEC 10Discussions on NCERT Solved examples and questions Chapter 2