sciencecapsules

    Consider a source of light like a candle.  The light (intensity) spread as the spherical wave .  We know  the brightness decreases as we move away from the candle.  We want to know exactly what is the intensity of the light  falling on the unit area at a particular distance from the source.  It can be obtained by dividing source's strength by the area of the sphere at that distance. Intensity on the unit area  = source's strength / area of the sphere                                         I=S/4𝚷R²                             R-Distance from source                                        I proportional  1/R²               since  S/4𝚷 is constant     S/4𝚷 is the constant so we understand that the intensity decreases as the distance's square increases or we can say, intensity of light is  inversely proportional to the square of the distance.  This is what we call inverse square law .      The inverse square law is applicable to gravitational, electric, magn

    We know the ratio of circumference to the diameter of a circle is pi= 3.14...  This ratio pi is applicable to a electron circling around a nucleus as well as to the planets revolving around the sun.  This mathematical number 3.14.. is a pure constant which always remains true.      If there are minimum 58 persons in a room, two persons will definitely have same birthday(not birth date) according to the probability theory.  This is also a proven truth.      The tangent of angle 45 degree is 1.  That is, in a right angled triangle of angle 45 degree, two sides will be equal. Tan 45 = 1= opposite side /adjacent side or opposite side = adjacent side. This can be applied to a triangle drawn on a paper or to the plane taking off at 45 degree angle. The mathematical facts like given above are always holds good for any persons,  anywhere and anytime.  Now let us consider some physics facts.  The acceleration due to gravity is 9.8 m/sec^2 on the surface of the earth.  But

  In todays digital world, the government can easily deposit one million dollars in everybody's bank account and make us millionaires instantly.  but it is not practically feasible.  Why ?  To explain it,I will go to an aid of an equation as usual.  First let us understand the factors that constitute the equation.   1. M= Total amount of money supplied among the people. For our calculation, let us take M as 100 dollars.  M is also the total amount of money present  the economy. 2. V =  velocity of money. That is, the number of times the M {100 dollars} is used {passed} among the people in year.  In our case, let V= 10. 3. P= average price of a good or a service.  Let it be 5 dollars. 4. T = Total  number of transactions or number of goods and services sold and bought in a year.  Let it be 200. T is also the indicator of economic activity.       M*V = Money supply * no. of times M used     Now the product M* V is the total annual spending by the people.              

      Our sun is a ball of fire.  Its flares  are extending to  thousands of kilometers.  It is in the middle life and produces such a enormous energy.  It is a small star and all the stars  are similar to our sun.       When a star is living it produces light and heat energy through nuclear fusion.  That is, by combining hydrogen atoms into helium atoms.  When the star runs out of the nuclear fuel, it will die.  During the death of a big star, its outer shell will blast off with such a brightness that it will be visible throughout the galaxy even in daytime.  This phenomenon is called 'supernova'. Next, star's inner core will get compressed due to gravity.  That is, star will collapse under its own weight.  It will collapse into a mathematical point called " gravitational singularity ".  All the mass is concentrated in that point.  Hence it will have zero volume, infinite density and enormous gravity.       The influence or the gravitational field of

EBOLA VIRUS     Imagine  a huge ship standing in the ocean near the beach and also a football floating on the ocean waves.  The waves does not care the football.  That is, the waves are not at all disturbed by the ball.  But the waves are deflected and reflected by the ship.  So the ocean waves "sees" the ship because it is bigger than the wave.  But the waves are "blind" to the ball because it is smaller than the waves.        A virus or  a group of molecules are having the size in the order of nanometer(10^-9m).  But the wavelength of visible light is in the range of 10^-6 to 10^-8 m. .  Since light waves are bigger than virus like object, it cannot see them.  Hence the optical microscope fails in this region.      So people turned to use other waves.  They found that the particle electron behaves like  waves.  Its wavelength is smaller than that of light (10^-10 m).  Hence electron microscope was built at very high cost.   Today we have variety of

    There was a chess competition in a king's regime.  The king promised gift of winner's choice.  After the game, the winner just asked some grains of rice  as his price.  He added one condition. He wanted to put one grain of rice on the first square of chess board;  2 grains on the 2nd square; 4 grains on the 3rd; 8 grains on the 4th one.  That is, doubling the number of grains each time till reaching 64th square.  The king was surprised by the humble request and ordered to execute the prize.  The servants brought sack full of rice and begum to arrange the grains on the board as instructed.  Halfway through the work, the king and the servants realized that all rice grains in his kingdom would not be enough to fill all the 64 squares.  The king submitted to the wisdom of the winner.  Then the winner said, "I do not want the price.  Just give rice food to the needy daily".  And he went away.  This is a good example for the 'geometric series' which is

Take the function, y = x^2 x        y=x^2 -3        9 -2        4 -1        1 0         0 1         1 2         4 3         9   If we draw the graph, we get a parabola.  Now we know how the function behaves.      I want to know if 'x' changes by 1[unity], What is a change in 'y' at any value of x.  That is, what is the rate of change of function at any point in the curve .  Is there any standard formula?  The question is easy to answer, if the function is linear or the graph is straight line.  The answer would be slope [gradient] of line and the slope will be the same at every point in the line. but Here we have parabolic relationship (refer figures).     Velocity is the rate of change of distance.Inflation is the rate of change of prices.Hence it is a very important quantity.      Here, calculus come to our help.  It tells and proves that  if y=x^2,  dy/dx = 2x;  that is, the rate of change of function y= x^2 at any point is x is 2x

    Take the point C[ -2+i] in the complex plane.  Let Z =0 +0i and square it. Z^2 = 0+0i..  Now add C = Z  to Z^2 and get Z1. Z1 = Z^2+C Z1 = [0+0i]^2+[-2+i] Z1 = -2+i now let Z=Z1 and calculate Z1 = Z^2+C  again     = [-2+i]^2+[-2+i]     = 1+5i [complex addition,multiplication used] Magnitude of Z1 [1+5i] = root of [1^2+5^2] = 5.09     Now do this repetitive feed back calculation say 100  times according to this formula.  Z[n+1] = Z[n]^2+C Each time calculate the magnitude of Z.  If the magnitude stay stable within 2 , paint the point C as black.  If the magnitude goes beyond 2 and heads towards infinity, either paint the point as white or the point may be given colours as follows.  If the magnitude goes beyond 2 after 10  iterations, the point C may be given red.  For 20 iterations, it may be a orange dot.  For 30  repetitions, C may be given yellow.  So the colours are chosen according to the programmers taste.     For all the points C in the complex p

                                  6CO 2 +6H 2 O  →   C 6 H 12 O 6 +6O 2                  CARBON DIOXIDE+WATER     →      GLUCOSE+OXYGEN                                                          [SUN LIGHT]   We know this is the reaction taking place in green leaves and is called photosynthesis.  In this article, let us see how important it is for our existence. 1.  Photosynthesis  and respiration are the two complimentary processes required to sustain life in a planet like earth. 2. It produces organic food from inorganic material. 3. Glucose produced in photosynthesis is used for plants growth and excess glucose is stored in fruits and roots.  Hence we get carrots, potatoes, apples etc.. 4. All animals and humans depend upon the plants for their food. 5. It converts solar energy into chemical energy 6. The dead and long buried plants and animals become coal, oil and gas due to heat and compression.  These fossil fuels are important sources of energy for us. 7.

      At present the world record for 100 m dash remains at 9.578 sec by USAIN BOLT.  Will it further come down?  Will ever a man make it under 9 sec.  We will try to answer these questions via mathematics.   Harmonic series:      Take a deck of 52 playing cards.  Move first top card to half of its length.  That is the maximum distance you can move before gravity pulls it down.  Now consider top first and second card as one unit and move both of them to 1/4 of the card length.  Again both will stay without falling.  Now consider first 3 cards as one unit and move all of them to 1/6 of the card length.  All the 3 cards stay put and we get some length of "overhang". Repeat the process for all the 51 cards.(last card cannot be moved).  The overhang accumulates as given by the following series. = 1/2+1/4+1/6+1/8+.........+1/102 = 2.2594........card length         We get a overhang of more than 2 card's length.  This arrangement seems to defy gravity.  Now

      The following phenomena may happen in near or far future according to the present scientists. Teleportation:       The ability to transport a person or an object instantly from one place to another is teleportaion.  If it becomes reality- cars, ships, airplanes and railway systems will go obsolete.   It  will revolutionize the way will live.  Atomic particles can be teleported at present.  Virus may be teleported within the current century.  But we have to wait for many centuries to transport a human being instantly.   Telepathy     Reading thoughts in  others mind  at will is telepathy.  If it is possible, you can guess the consequences.  Today, by taking MRI scan of the brain, a doctor can explore its function.  One day. science may develop hand-held brain-scan machine using which we can read others mind. Psychokinesis       Moving and manipulating an object using just pure thought is psychokinesis.  For example, bending a metal spoon with mind power.  

    What is the probability of getting an odd number in a dice throw?  There are three odd numbers 1,3 and 5.  Hence the probability is 3/6=50%. Draw a circle within a square   Drop pins randomly in the square.  The pin should fall on its tip.  What is the chance of pin falling within the circle? Area of the square = 2r*2r= 4r^2. Area of the circle = pi r^2. Hence the chance of a pin falling in the circle = area of the circle/area of the square.                                                                          = pi*r^2/4*r^2                                                                          = pi/4 = 3.14/4 = 0.7854                                                                          =78.54% Hence the pin mostly will fall within the circle.      Let us assume that you are waiting in a queue in the doctor's clinic for treatment.  Let us further assume that the waiting time varies between 0 to 45 minutes and the treatment time varies between 0 t

    Toss a coin 100 times.  You are likely to get head around 50 times.  So there is a 50 % chance of getting a head or a tail. In other words, the probability of getting a head or a tail is 1/2.  The range of probability is 0 (no chance)   to 1(100% chance).        Suppose you toss a coin 3 times, what is the chance of getting a head in all the 3 throws.  Here the multiplication rule comes to our help.  This rule can be applied when the events are independent of each other.  Just multiply the probability of the event 3 times.  total probability = 1/2*1/2*1/2=(1/2)^3 = 1/8 = 0.125  The probability of getting only heads 3 times consecutively is 1/8 or 1 in 8.  That is , if 8 persons throw the coins 3 times, 'one'  may get the head all the three times.        Let us assume that in a multiple choice question, there are 4 choices and one among them is correct.  Guessing that correct answer has a chance of 1/4.  If there are 10 questions, what is the probability of gu

   When a heavy wind blows over a hut with thatched roof, the roof just blows up.  When the air flows fast, the pressure drops.  Hence air pressure decreases over the roof; the pressure under the roof becomes greater and it lifts off the roof.  This is due to Bernoulli's principle.      Bernoulli's principle says, as the velocity of fluid increases, its pressure decreases .  This principle is also used to measure human blood pressure.         When the planes runs very fast, the air flows fast over the wings and it flows slower under the wings.  It happens because of the geometry of the wings.  Hence there is more pressure under the wings and it lifts up the plane. There is a formula for the lift of the plane. L = 0.5*C*D*A*V^2 V- velocity of the plane. A- area of the wing. D- density of the air. C- constant due to wing design. L- lift      The Boeing 747- jumbo jet requires a lift of 2150000 N(upward force).  This lift will cancel out the huge weight