SCIENCE CAPSULES

         We know, just 2 numbers (x,y) are enough to mark a point in a graph sheet or in any surface.  Can we find the distance of the point from the origin just using these two co-ordinates?  Here the Pythagoras theorem comes to our help.  Since x and y co-ordinates indicate horizontal and vertical distance of the point from the origin, square both of them; add them and take square root.  We get the diagonal distance from the origin.                  r^2 = x^2 +y^2      Pythagoras theorem is the first topic in any math book.  It still reigns in math and physics world.  It's importance will never fade with time.      Suppose we want to find inner diagonal in a rectangular box, it can be found using the formula given below.  We should remember the box is a 3 dimensional one.    Diagonal^2 = Length ^2 +...

First, a quick intro to sine wave. Y = sin(x)  or Y = A sin(2pi*n*t) A- amplitude n- frequency t - time      The above function describes (a graph) a simple and neat sine curve as the time progress.      Take two such waves and add them or superimpose one on the other(interference). Mathematically    Y = A sin(2pi*n*t)+ A sin(2pi*n*t)    Y = (A+A) sin( 2pi*n*t)     Here the amplitude doubles.  We get a bigger wave.     Now subtract both the waves. Y = A sin(2pi*n*t) - A sin(2pi*n*t)    = 0 The waves cancel each other. Figures are given above. Take two sine waves of slightly different frequencies and overlap them.      Y = A sin(2pi*n*t)+ A sin(2pi*(n+m)*t)     m = 1 or 2     If one draws a graph for the above function, a beautiful wave pattern results.  It is called beats.  Suppose, the two waves are sound wa...

1.   E = mc^2      This equation does not require any introduction.  This equation says energy and mass are one and the same and one can be converted into another.  This formula is responsible for atomic energy.  Today's nuclear reactors and atom bomb arises from it.  This Einstein's equation will always occupy top pedestal in science. 2. ds >  0          This is the second law of thermodynamics.  The energy always flows from higher concentration to lower concentration.  For example, heat energy always flows from hot body to cold body.  Also the law means that disorder(energy) always increases.  This law made possible the invention of internal combustion engine. 3.       This is the Schrodinger's equation.  This function treats sub atomic particles as waves.  It gives probability and fuzziness to atomic particles .  Hence it gav...

         A fast running bi-cycle hit by an object may not fall down.  It gets stabilized due to gyroscopic effect.  A boat or ship tilted by the strong wind will not turn turtle because it is so designed to stabilize itself.  A space station orbiting around the earth may get hit by a rock.  It may slow down.  But it will not plummet to the earth.  It automatically get stabilized.  Let see how.      A satellite is taken by the rocket and pushed into the orbit.  The satellite is given a preciously calculated velocity called 'orbital velocity'.  If the velocity is slightly less than the orbital velocity, it will fall down on the earth pulled by gravity.  If the velocity is more, it will fly away from the earth or earth's gravity.      Any orbiting or rotating body have what is called "angular momentum'.  given by the formula      Angular momentum = mass * v...

         In this essay, let us take some time to wonder about our own planet.      As for as we know, this is the only and lonely planet which sustains life.  When it is looked from the moon, it appeared like beautiful blue marble.  It has little habitable land and more ocean waters.  It shelters wide spectrum of plant and animal life.  It is not like a moon which is a boring and barren land.  It has oceans, dessert, rivers, waterfalls, valleys, farms, vineyards, mountains, forests, lakes and so on.      The earth yields flowers of many colours, designs, and smell.  We can grow sugar cane and hot hot chilli side by side.  It is wonder that the same earth yield so much variety, spice, colours, and tastes.      All the 100 plus  elements in the periodic table can be mined out of earth's surface.  It yields so much iron and hydrogen but little gold and uranium. ...

         Age of universe is said to be about 13 billion years.  It can be estimated using the Radio-activity in a piece of rock.  The entire universe was said to be contained in an atom 13 billion years ago.  An explosion occurred (big bang) and the entire universe was thrown out and started spreading.  The universe continuous to expand even today.      Age of the earth is around 4.5 billion years.  It is born out of sun and belongs to the solar family.  It  has undergone so many changes since its birth.  Even old continents have gone and new continents have formed.      The first man had appeared around 2.5 million years ago.  The first single cell life appeared in the ocean and evolved into intelligent human beings according to Darwin's  theory.      The mutations and environment necessity made us.  We are now dominating the world in using its re...

         Imagine a balloon full of air.  The air molecules are moving randomly inside the balloon.  Let us pierce the balloon with a pin.  The air rushes out.  Why should not the air molecules stay inside the balloon safely and ignore the little hole?  That is not the way the world works.  The molecules always "want to occupy as many states as possible".  Hence the air goes out in the open to occupy more volume.   The things always goes into disorder (entropy) and the disorder increases with time.  The above statement is what we call "second law of thermodynamics".      Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze.  Freezing means bringing things to order and arrangement.  It violates the second law.  Hence it will never happen.  Hence heat must flow from high ...