SCIENCE CAPSULES

    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               sin...

    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 ac...

  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   ...

      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 ...

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^-...

    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 i...

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 pric...