sciencecapsules

    If house is left without maintenance for some time, it becomes dirty and cob-webs accumulates.  If left for a long time without care, the paint peels off, cracks develop and some bricks fall off.  If left for hundreds of years, it will become a ruin and may get buried in the earth due to gravity.  Hence, as the time progresses, the disfigurement, damages, disorder increases.  In any system, the disorder or randomness increases with time, if left uncared.  It is called entropy in physics and it is governed by second law of thermodynamics.       But why it happens?  There are certain ways to construct a house{orderly arrangement}.  But there are millions of ways for disarrangement.  That is, more chance for disorderly arrangement of bricks, cement, iron bars etc,.  So naturally the house will go into disarrangement easily.  Here we can conclude that the disorder or entropy is a  'measure of elapsed...

      Light and eyes gives us 70% of our knowledge.  Hence we should have some knowledge of light.      Sun's rays, LED glow, candle flame, festival sparklers.  What is light?  How it is created ?  Let us explore.        We know electrons are circling in the atom.  Electron absorbs some energy and goes to high speed orbit.  Analogy:  Let us raise a stone from the ground to a certain height .        The electron fall back to the low speed stable orbit.  While it moves to lower orbit,  it follows slightly spiral path and its speed decreases.  Consequently the electric field associated with it{electron being a electric charge} changes and creates changing magnetic field perpendicular to it.  In a nut shell; when the electron jumps from higher energy level to lower energy, an electromagnetic disturbance is created.   Let us drop the stone in a water b...

     Majority may follow the rule.  There may be a few exceptions.  Exceptions does not disprove the rule.  But  prove it strongly. 1. All living beings follow a life cycle.  They born, grow, multiply, live and die.  But  virus never dies.  It  always spring back to life in watery environment.   2. Normally  insects eat plants.  We use pesticide to  kill them.  But there are plants which capture and eat insects. 3. All  shapes have two sides.  That is, inner and  outer surface.   Take a ribbon of paper.  Give it to a half twist.  Paste the ends together.  It is mobious strip and it has only one side.   4. Normally  we deal with whole numbers in our daily life.  50000 rupees of salary, cost of 320 dollars, height of 172 cm.   But nature does not deal with such sharp numbers.  The mathematical constants pi = 3.14.. and e= 2.71.. are ir...

 Long long ago, there was a prince.  He was wandering along with his assistants through the forest of his land.  He came across a small house.  The smell of butter melting into ghee wafted from the house.  The prince concluded that there must be a woman in the house.  He asked his assistants to knock the doors and get a cup of water.  When the door opened, there appeared an angel like girl.  The prince instantly got attracted and tempted by sculpted beauty.  The girl sensed danger.  She ran out of the house through the back door.  The prince and others chased her.  She ran helplessly and prayed intensely to God to turn her into stone at once.  And she friezed into stone.  The time went by. "she" become the goddess of her village.  She is worshiped even today.  So the story goes.      If I had the story in my childhood, I could have enjoyed it and gone to sleep.  If I happened to r...

    Butterfly is beautiful because of it's symmetrical shape.  Almost all natural objects have symmetrical shape.  Humans , animals, plants, moon, mountain, seashells, snowflakes, egg, DNA etc,. There are many examples in mathematics. *Shapes like parabola, cone, square, circle, etc,. *Every operation has a reverse operation. + to - x to / a=b^c to c= log a   to base b *Even the mathematical objects called fractals which are arising out of chaos exhibits symmetry. Symmetry is abundant in physics. *To every action there is and equal and opposite reaction. *Heat can be converted into work and vice versa. *Energy to mass; mass to energy. Both conversion possible.   *If magnetic dipole has north and south pole, electric dipole must have positive and negative poles. *If changing magnetic field creates electric field then changing electric field must create magnetic        field. *In a motor, we send current and produce...

 You may not marry the first man or girl you meet because you may get a better one later.  You cannot also wait for a long time till your hairs become gray.  So what is the optimum time you have to wait?  or what is the optimum number of persons you have to scrutinize?  Here mathematics comes to our help.      Let us assume that you are able to  encounter  'n' {say 60} persons as your prospective bride or groom in a span of one year.      Say, you come across a first person.  What is the chance of selecting him or her ?  Also what is the chance of rejecting?  The probability theory says the chance of selecting is 1/n =1/60=0.017.  The probability of rejecting is [1-1/n] =[1-.017]=0 .983      You come to know a second person.  What is the chance of rejecting both.  The multiplication rule tells it is, [1-1/n]* [1-1/n] = 0.983*0.983 = 0.966. If you meet 3 persons in ...

    Suppose you are given 4 symbols A,1,B,2, how many passwords you can make with them or how many different arrangements are possible with 4 symbols. Examples:1A2B, 12AB, AB12, ......      First place can be taken by any of the 4 symbols.  So 4 arrangements are possible for first place.  Second place can be taken by remaining 3 symbols {3 arrangements}.  2  arrangements for third place  and only one letter is left for last position.  Hence total number of arrangements is  4*3*2*1 = 24=4! =factorial 4.     So factorial N gives the total number of arrangements or permutations possible with N objects.  There are 52 playing cards, we know.  Each time you shuffle, you get a new arrangement of cards.  How many arrangements are possible? 52! = 25*51*50*.........2*1. =        = 8.066*10^67 8 followed by 67 zeros. Here the total number of arrangements  of cards is unimag...

    In any artificial and natural growth at some rate, the quantity will double at regular intervals of time- doubling time .  In any decline or decay process at a fixed rate, in the quantity will halve itself at constant intervals of time- half life .      For example: at a particular rate of interest, the amount of money will double in constant period of time.There is a very simple formula to calculate doubling time or half life. Doubling time or half life = natural log [2] / rate of decay  or growth. simply                         t = 0.6931/r Note:  Rate should be expressed in decimal numbers. example: 5% = 5/100 = 0.05 the answer will be in the same unit as r considering real life problems: 1. If the inflation rate is 6% per annum, when the prices will double?    t = 0.6931/0.06 = 11.5 years Every 11.5 years, the prices will be double. 2. If a financi...

Take this 4 letters O,P,S,T.  How many meaningful words one can make with them?  I can make 6 words. Post, stop, tops, opts pots, spot. Actually how many words one can make with 4 letters.  It is mathematically given by factorial 4 =4! 4*3*2*1=24. Hence 24 words are possible.  Some may be meaningless.  How many 4 letter words one can coin using 26 alphabets.  There is a permutation formula to calculate it.    26! /[26-4]! = 26!/22! = 358800  Hence we can make 358800 words. { many words will be meaningless.}  In addition to this, we can coin many 2 letter, 3 letter, 5 letter and so on words out of 26 alphabets.  But the 20 volume oxford dictionary contains only 171476 entries.  So we can understand that there is a room for many more new words.      Similarly using the available words, we can coin many many new sentences.   For example:     On reaching my house, I found the keys w...

      It is a Sunday morning.  You are sitting in a easy chair with a news paper in one hand and a hot cup of coffee in another.  The tree lives are still.  No ripples in the nearby pond.  No traffic. And you think everything is at rest, quiet and still.  It is actually far from that.      When you lay still, you heart is throbbing 72 times per second pumping 2000 gallons of blood per day  through 60000 miles long blood vessels.  Your lung inhales and exhales air continuously.  And there are so many biological processes are ON in your body.     The liquid molecules in the hot coffee are at fast random motion.  The news paper you are holding is made up of hydrocarbon.  The electrons in these atoms are whirling around the nucleus and the protons are spinning.     Thousands of elementary particles called neutrino from cosmos are passing through your body at this instant. ...