sciencecapsules

        Let us say, you are buying 10 chocolates for 20 dollars.  If you divide 20 by 10, you get 2.  So 2 dollar is the price of 1 chocolate.  Division always gives the rate.  In this case cost per unit.      Another example:  a car covers 120 km in 2 hours.  120/2 = 60 km, It is the speed of the car.  Also rate of distance traveled by the car.  (distance traveled in one hour)      In general Division y/x, gives the value of y when x is unity.     Now let us assume that, we have two series as follows. x = 1,2,3,4,5,6.... y = 1,4,9,16,25,36...    = x^2 Here, I want to find y/x.  But the values are not uniform and  they are growing.  What to do?  Here calculus comes to our help.     It says, if y=x^2, then y/x or more correctly   dy/dx = 2x. Let us verify, x = 3; y = 9 x  =4; y=16 For unit change in x(4-3=1), the change in y is 16 - 9 =7 The average of x = 3 and 4 is 3.5 So 2x=2*3.5 = 7 Hence, for unit change in x, the change in y is 2x - verified. For functi

          One fine morning, you wake up in the middle of dense forest.  You do not know where you are?  But luckily, you have a FM radio set.  Tune the radio, you hear one station feebly.  You know the location of that radio station.  The maximum range of that FM station is 100 km (say).  You must be at the edge of 100 km since the FM signals are weak.  Now, you draw a circle with that radio station as the center and 100 km as radius.  You must be somewhere on the edge of the circle.     Now try for another station.  Luck favors you again.  You get second station that too feebly.  Now this station as center, you draw second circle of same radius.  Now the two circles meet at two points. You may be on any one of the point.  Still the information is not enough.  Try your luck again.  The God of luck is still with you.  You get third FM station some what clearly.  Draw third circle as usual.  The three circles meet at one point.  Thank God, that is your location.  This is known a

              When I say, sound waves can bend, it cannot be observed in open space.  Suppose, a man speaks from the stage in a hall and you are standing outside the hall.  You can still hear his speech.  It proves that the sound waves bend around the doors and windows and reach you.  Wavelength of sound and width of door are comparable.  Hence the bending of waves or diffraction can easily be observed.     The light waves are very very small.  So its bending cannot be observed through house doors.  So we have to construct small slits suitable to it's wavelength.     A piece of glass is taken and using a diamond needle, so many lines (rulings) are drawn on it.  Nearly 5000 lines per mm.  The rulings are opaque and the space between the rulings are transparent.  Hence they act as 5000 slits per mm.  Now the slits are comparable to the size of light's wave.  This device is called 'grating'.     If the light is passed through grating, it will bend at all the th

        When a running ball hit a ball at rest, the latter starts moving and the moving ball comes to rest (when they have same mass ).  Here the energy is transferred from the first ball to the second due to impact.  The collision plays an important role in physics.      When a ball hits a wall, the energy cannot be transferred to the wall because of its heaviness.  Hence the ball bounce back with the same speed and the energy.     The proton and neutron is having the same mass.  This concept is discovered using collision as in the ball example.      The 'light' particle photon collides on metal like zinc.Cconsequently an electron is ejected out.  This is the photoelectric effect widely used in electronics.     If the air molecules collides on the walls of the container(tubes and balloons) like balls on the wall, it gives raise to pressure.  More air, more collisions, more pressure.     When a meteor hits a planet, the energy gets dissipated and creates a crate

               Today, using satellite technology, we can accurately measure the circumference of earth.  But hundreds of years ago, people had measured circumference approximately just using sticks and shadows.      Now, choose a place in the earth at which you get no shadow around noon. (not all places, throughout the year gives zero shadow at noon.  You have to do some research to find that proper place and proper date). CHENNAI OBSERVED ZERO SHADOW DAY ON 24-04-2018.--THE HINDU      At that place, and on that day, you fix a stick A (say one meter long).  Ask your friend to fix another stick B of same length at some location which is hundreds of kilometers away.  When you get 'null shadow' at some instant, your friend will get some length of stick's shadow due to earth's curvature. (refer figure)      At the time, when the stick A's  shadow vanishes, ask your friend to measure stick B's shadow. (of course, through phone).      Now, come to th

      Say, 'A' has so far won 60% of the games (chess, shuttlecock) he participated.  But 'B' has won only 40% of the games.  If A and B clash in a game, clearly A has 20% winning edge over 'B'.  But , if luck favors B,  A may lose.  So one game is not fair enough to decide the winner.       Suppose A and B plays a set of three games, whoever wins any two games out of three is a clear winner.  Let us see the maths behind it.      What is the chance for A to win any 2 games out of 3.  There are four possibilities or pattern to win.  Pattern1. Win, win, win Pattern2:  win, win, lose Pattern3. Lose,win,win Pattern4. win, lose, win      The winning probability is 0.60 and losing probability is 0.40 for A.  Hence substitute the probabilities and use multiplication rule of statistics. Pattern1. .60*.60*.60 = 0.216 Pattern2. .60*.60*.40 =0.144 Pattern3 .40*.60*.60 = 0.144 Pattern4. .60*.40*.60= 0.144        Total winning probability = 0.648    

        When a running fan is viewed under tube light, it appears to rotate backwards or forwards.      Our houses are supplied with alternating current of frequency 50 cycles per second.  That means, the current is 'on' for 50 times a second and 'off' 50 times a second.      Our eyes has the property called 'persistence of vision'.  It means, whenever we see an object, it's image is retained in the eye for one tenth of a second.  No image in the eye vanish immediately.  Due to this property, our eyes do not perceive flickering of the electrical lamp which arises because of alternating current.      Say, now you are viewing a table fan under electrical lamp.  When light (current) is 'on', a particular image of the fan blade is recorded in our eyes. When the lamp is 'off' for some milli- seconds, the fan blade  might have rotated by an angle to a new position.  The new position of the blade may be in forward or backward to the origi

        First, let us take a 4-digit PIN.  Let us also assume that a man is attempting to steal it.  To get the first digit right, he has to try all the 10 digits (0--9) and 'one' will be correct.  So the chance of getting correct first digit, is 1/10.  The ' Multiplication rule in probability' says that the chance of getting all the four digits right is 1/10*1/10*1/10*1/10 = 1/10000. It means, if he makes 10000 tires, at one instant he will get the correct PIN.  But the bank allows only 3 tries and limited time.  So the PIN is safe as long as you keep it safe.     Now our financial transactions depends on the password.  Let us see, how to strengthen the password.      Let us consider a 7 character password which can take alphabets and numerals.  The total number of characters is 26+10= 36.  The chance of getting any one character right is 1/36.  As usual, the chance of getting all the seven characters right is 1/36*1/36*1/36*1/36*1/36*1/36 *1/36 = 1/36^7 = 1/

         If you toss a coin, the chance of getting a "head" is 50%.  That is , chance is 1/2 or 0.5 ( That means, if a coin is thrown 2 times, you will likely to get one head or if you toss the coin 100 times, you are likely get 50 heads ) .  The probability of getting any one (head or tail) is 100% or 1.  The probability of getting no head and no tail is zero.  Hence the limits of probability are 0 (no chance) and 1 (guaranteed).  The chance of  drawing " king of diamond" from a deck of cards is 1/52.  The chance of rolling a 'Three' in a dice game is 1/6 (since six faces).  Thus goes the probability.      Can a child, a monkey or a blind folded man (without the knowledge of typewriting ) type a word or two correctly? Can a computer write a poem?  let us see.          Let us take two words NO and YES.  What is the chance of typing 'N' randomly.  We know , it is 1/26. The chance of typing 'O' is also 1/26. Then, what is the chance of

         Long ago, In astronomical calculations, people had to multiply and divide large numbers.  They wanted to find an easy way out.  And Napier's work in this direction gave birth to Logarithms which made computation easier.  Let us explore the concept. Consider, 1,2,3,4,5,6      This is the sequence of natural numbers and also called arithmetic progression (A.P)      2,4,8,16,32,64...      In the above series, the ratio between successive number is 2.  And it is called Geometric progression(G.P).      Now, if you want to multiply or divide the numbers in G.P, Add or subtract corresponding number in A.P and then find the corresponding number in G.P for that answer. Example: To multiply 4 and 16, in G.P Add 2 and 4 in AP 2+4 = 6 Corresponding number for 6 in GP = 64 verified 4* 16 = 64 To divide, subtraction should be followed.    ------------------------------ So multiplication and division has been reduced to simple operations addition and subtraction. We can understand