GENERAL PROLEM SOLVING TECHNIQUE
2. Guessing simple Concept
One good problem is linked with many simple concepts .This mix gives us is, an tricky looking question.Your first effort should be, to read(mark the catchwords) and somehow break the question so that you can identify(better word would be ‘guess’) the simple concepts involved .For identifying simple concepts, one must resort to drawing small diagrams of the problems and then a careful thought procedure should follow.Once you have identified the simpler concepts involved in it, then goto stage number two that is linking the concepts.Now this linking stage is where your earlier efforts and mental level come to the fore, in this area of linking no one can help you
except, you, yourself.In linking you use result of one portion and apply it to solve another.We will illustrate all these stages with an example:
JEE APPROACH: Remember , our aim is to show you method of attacking a problem by the above analysis , hence we will give an essay type description.
1.1. ‘uniform disc’ , ‘round cut’,‘passing through centre of inertia’….
2.1. ‘ uniform disc ‘=> AREA proportional to MASS
2.2. ‘round cut’=> area removed=> proportional mass removed..leads to depletion of Moment of inertia…..also center of gravity of remaining disc will not be the at the same position as of full disc.
2.3. ‘ passing through the centre of inertia’=>maybe parallel axis theorem ….!!!!???
Remember ,practice makes you a ‘better linker’.What you get by solving good number of problem is EXPOSURE which makes you a better linker.Back to the problem…
=>(M/(pi*R^2))pi(R/2)^2=M/4.Mass of remaining portion is,m = M-M/4=3M/4
MI of full disc about CG of remaining disc is [MR^2]/2 + [M(0 -Xcm)^2]=19(MR^2)/36
=> MI of remainig disc = MI of full disc - MI of removed(small) disc=37(MR^2)/96=37(mR^2)/72 Ans.
SOLVING OBJECTIVE TYPE PROBLEMS
THE "HALL EFFECT"
Last few weeks and ofcourse the examination day and the night before has a determining effect on your JEE performance.This analysis focusses upon various factors that effect your performance on the examination day.Read the given description carefully ,it contains 7 blunders which one commits on the examination day, try to spot them.
Its the day of your exam you wake up in the morning and reach for your notes to revise a few points quickly.There is lot of activity seen at your home , your parents are looking as much corncerned as you .You can very well hear your heart beating and you are in a very serious and nononsense mood.Your are keeping a note of your examination time .Now you are ready and your mother comes and puts a ‘teekaa’ on your forehead , she says "son this is a very decisive day of your life may god help you", your touch the feet of your parents……"Now my brave soldier you are ready for the fight" the situation implies.
You pick up your conveyance and start to move towards the examination hall.In the way you are worried about your performance ,"How will the paper be?","Will i be able to solve adequate problems","i could have studied more..","Its THE EXAM of my life…what if i am not able to do up to the mark?"..all these are coming to your mind.
Finally , from a distance you are able to see your "battle field", you can see the board of the examination centre "BNSD Vidya Niketan", your pulse rate accelerates.Outside the centre you see lots of parent and aspirants moving here and there(total brownian motion!!),some are moving inside , some coming out , some touching the feet of there parents and parents wishing them best of luck.Everybody has his own "Astra" in there hands.There is this guy in blue jeans , he is sitting and looking at his notes ,you are inspired and you also start thinking about looking at few formulas.Meanwhile you see Rajesh , who is there in your coaching , you start to talk with him.
There are lots of guys ,crowding that area.You go there and find that room allocation is displayed , your room number is 7A.You enter the room, there are few guys in the room.You search for your seat and then do a quick inspections of it to see whether everything is fine or not.Now you sit down and try to make yourself comfortable.
After a while two serious looking invigilators come into the room , one is holding answersheets and other is holding a brown packet that contains your question paper.Your heartbeat again increased due to the realization that the papers have finally arrived.You stare at the packet , wondering what type of paper might be inside?.You are given the answer sheet with the instruction to write your name on it.
Finally , you hear the grand bell ring, with every ring you get a very strange feeling in your heart and stomach.Invigilator starts to distribute the paper and you are waiting for your turn to get it.You strart attempting the paper.You looked at the seat where Swami(an intelligent boy of your coaching) is sitting , you saw that he has already started attempting the paper while you are just trying to find out which question to solve.Now you have finally started attempting the paper.Time passes and finally ends.
After submitting your paper you rush quickly for your pencil box and writing board.You have next paper after a break of 1.5 hours.As you move out of the room you see a lot of commotion.You see guys discussing about the paper, you overhear there talks…"yaar paper was easy compared to last year ….cutoff will be a little higher" , "hey what was the correct answer of that Uranium 238 problem…i think it was option c..what do you say","most of the questions in maths came from XYZ’s book"etc. etc..You are also very anxious to know how Swami and Rajesh performed in the paper so you go and discuss the paper.
After discussing the paper for about fifteen minutes you come back and have some snacks while you plan to revise a few points for the paper after an hour.You revised till it was time for your next paper.You proceed towards your exam room once again…..
COMMANDEMENT#1 MAKE SURE THAT YOU DO NOT PICK UP PRESSURE FROM YOU HOME
COMMANDEMENT#2 YOUR USEFUL MENTAL ENERGY IS FINITE , SO CONSERVE IT!
COMMANDEMENT#3 KEEP YOURSELF IN A WATERTIGHT COMPARTMENT.
COMMANDEMENT#4 REHEARSE EXAM DAY EVENTS IN YOUR MIND BEFORE THE EXAM DAY.
COMMANDEMENT#5 CONCENTRATE ON THE PAPER.
COMMANDEMENT#6 DONT LISTEN TO WHAT OTHERS ARE TALKING AFTER THE EXAMS…KEEP YOUR EARS CLOSED ..IF NEED BE USE A EARPLUG!
COMMANDEMENT#7 DONT DISCUSS THE PAPER IF YOUR EXAMS ARE STILL ON ,IF POSSIBLE TRY TO REST IN THE BREAK.
Any good IIT-JEE like problem , when analysed contains basically of three parts
IRODOV 1.241A uniform disc of radius R=20cm has a round cut as shown in the figure .The mass of the remaining portion of the disc equals m = 7.3kg.Find the moment of inertia of such a disc relative to the axis passing through its centre of inertia and perpendicular to the plane of the disc.
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2.guessing simple concepts:—-
3.linking and solving the problem:—-
Taking clue from 2.1, suppose you had the full disc , if we remove the portion then the area removed is pi*(R/2)^2 => mass removed
Taking clue from 2.2, we have removed a disc of radius R/2 from the orignal disc , so if we remove contribution to moment of inertia of that disc from full disc we will get the moment of inertia of the remaining
Next we try to find the center of gravity(CG) of the remaining portion .The CG of small disc is at the center of the small disc and that of full disc is at the center of full disc(our origin)….full disc=small disc + remaining portion!!! .So CG of small disc*its mass + CG of remaining portion*its mass = CG of full disctotal mass(equalising the mass moments) gives: (R/2)(M/4) + (3M/4)*Xcm=M0 => Xcm= - R/6
Taking clue from 2.3, moment of inertia(MI) of removed disc about ITS OWN CENTER is [(M/4)(R/2)^2]/2 , and about the CG of remaining portion is [(M/4)*(R/2)^2]/2 +(M/4)*(R/2 -Xcm)^2 =41(MR^2)/288
try to see the’ linking’ carefully ,see how results of 2.1 is used in 2.2 and then in 2.3 to arrive at the solution.
In future , try to proceed by the above procedure and you will be able to win over lots of problem !!!!
If you know these points then it will improve your performance
It is not the famous "hall effect" of physics that we are going to talk about.We are going to talk about how the examination day itself effects you examination performance.So you are thinking ,"what the hell examination hall has to do with our JEE exams?",well then to answer you , it can make you spoil your paper or it can help to accelerate your efficiency and hence your performance.
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We gave this long discription to bring you closer to the feelings and activities of your examination day.There are seven blunders committed by "you" in the above given passage.click on the button below to see those regions.
The first center from where you start getting pressure is your own family.Dont let the pressure of expectation from your people, build upon you .If you will be treated as a brave soldier going for his fight then there will be a lots of pressure upon you.Ask your parents (while fully caring for there but natural feelings) not to make you feel as if you are going some very big event because that makes you conscious and puts a lots of pressure on you , since they have love and care for you they will surely understand it.Also ask them clearly , not to ask you "how are your papers going?","How did you perform" etc. till all the papers are finished.
Dont bother yourself with things that you can not control ,like,"How will the paper be?","Will i be able to solve the problems?".Remember , you dont have infinite source of energy ,lets say you have 100 units of useful mental energy on the day of your examination ,now if you worry about things you have the least control you loose say 20 units so you have just 80 units left for the paper .The other guy with same mental capacity as you and who stays away from these useless thinking will have 100 units for his paper , dont you think he will perform better.
The third centre of pressure is when you reach the examination centre .You should try not to observe other people too much,try not to talk to your friends,sounds uncourteous!, but still dont talk.The reason for this is that at that time you are in a "unstable state" ,even a little "perturbation" can cost your performance,so policy of isolation is best for you.
The fourth time where you get useless pressure is on the arrival of the invigilators .Dont look at them or the there activities.Close you eyes and relax.We advice you to rehearse all these events much before the exam day ,in your mind ,that will help in making you feel easy on the exam day.
Once paper is given to you,you should concentrate on the paper.Dont try to look what others are doing bacause 99% of times you will harm yourself by looking here and there.
We can bet anything on this !!.You will find at least one guy if not many , who will claim that "paper was easy…cutoff will be high" or "xyz question came ditto from pqr’s book","i could solve only 70 out of 90 ,will it be sufficient".Actually most of the guys who say these types of thing have low confidence on there performance and hence to get a momentary "high" by speaking these type of thing , they are only attraction gatherers.Since you dont know this dirty game of these imposters you start to believe them and put yourself on pressure once again.If there is a paper to follow you performance will surely depreciate.
If you get break between two papers you should not waste it by discussing the previous paper , you should take time out to rest for a while.