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These are a set of instructions with proven track record
These are not intended for students who score more than 90%, but for those students who score less than 40%. This will help the students to score more than 60 – 80% depending on how much you are able to follow the directions.
Following the guidelines will help you prepare yourselves to score more with a few days of hard work!
Gravity, one of the four main fundamental forces in nature. It is one of the most commonly observed forces in nature and yet it is as still one of the least understood of all forces.
Gravity was brought into fame by this famous apple shown above when it garnered enough strength and weight to detach itself from the tree and land on Newton’s head. This triggered his brain cells into thinking what made the apple fall down and thus Newton penned the theory of gravity.
The formula of gravity as given by him was:
And although he made the theory of gravity in a real short while it took him
twenty years to publish it in his book.Why? Because he had to prove that the mass of an object lies at it’s centre and for that he had to develop calculus to such a point that this could be proved. So in a way that apple was responsible not only for the discovery of the theory of gravity but also the the development in the field of calculus.
But why did newton have to prove that the mass lies at it’s centre?
Take a look at the above picture. Now if you see the formula you would see that given no action of any external forces the two bodies would attract each other with the force that is inversely proportional to the square of the distance between them. But what is the exact distance between them. Because mass can be distributed over a large volume. So if the two bodies touched each other the force of gravity is supposed to be infinite right? Because the surface has mass and the mass is at zero distance from each other. Well that’s what the mass being concentrated at it’s centre means. The force of gravity is taken by calculating the distance between the centres of gravity of two continuous volumes of masses. That way no matter how close or how small or heavy the objects are they would never make the distance zero. Think about it!!
This theory was an absolute success as it was a unifying concept that not only explained the free fall of apples towards the earth but also the movement of the planets around the sun and the movement of galaxies and stars!
Of course the problem was that nobody including Newton actually understood what gravity was!They knew it was a force but the origin or the behaviour of this force still remains unknown.That’s when Einstein made his epoch making theory of special relativity and also the general theory of relativity.
Einstein made a simple observation. He already found that nothing can exceed the speed of light from all frames of reference via his theory of special relativity. Then he put up a thought experiment. He supposed that the sun would suddenly disappear. In that case the force of gravity keeping the earth in it’s orbit around the sun would just disappear too. But the light from the sun takes 8 minutes to reach the earth. So in that case we would still see the sun and yet we would not feel it’s gravity. That leads to the conclusion that the effect of gravity reached the earth faster than the speed of light! But nothing can travel faster than the speed of light. This apparent contradiction led him to modify the theory of gravity a bit. While there was nothing wrong with the magnitude of gravitational force it was the way the gravitational force lines acted that was changed.
Einstein said that gravity was the effect of bending the geometry of the space around it that led to the observation of a force acting.
Look at the above diagram. Suppose the the black line represents the path along which it is possible to move also called a dimension.
If we move both one will travel in a straight line while the other will travel in a bent line. If the lines become invisible it will seem as if the the object on the straight line is under no force but the object moving on the curved line is being pulled by a force that is changing it’s direction.
This is exactly what einstein called it. He said gravity bends space in such a way that it seems like a force.His theories were tested and proven multiple times and they were almost always found to be true. He was truly a remarkable genius since he explained a fundamental force through geometry!
Now fast forward to the present we have new theories called standard model, string theory etc. However they still find explaining gravity a mystery! Yes what is gravity has been found but what explains it’s origin is still a mystery! While the world might be rejoicing at finding the higgs boson the boson does not explain gravity. And though string theory does predict it , the theory itself is yet to be verified by the scientific community.
Of course nowadays newer more expensive equipment are being created which sought to find the elusive particle of gravity called gravitons. And hopefully we will fully gain an in-depth understanding of gravity one day. Maybe one day the unknown apple shall fall on someone’s head again and we shall be saved from the ignorance of that special force called gravity!
Most of you might know einstein as being synonymous with genius. Yes he is the epitome of creative science and is still regarded as idols by some of the finest scientists of the world. Even the top most scientists considered him as being a revolutionary as his out of the box thinking. Today we are going to touch upon his theory of special relativity.
Right so first we shall discuss a bit about relative speeds.
Let us suppose that there be a system of two bodies named a and b respectively which were moving with velocities va and vb respectively towards the left. Now if you were standing on the ground at rest you would notice that both moved towards the left with velocity va and vb respectively. However if you were on the object a you would notice that the velocity of b looks to you like va-vb towards you(towards a) (here we are considering that va>vb)however if you were on b you would notice that b is moving towards you with velocity vb-va. Now if one of the objects were to be accelerated and supposing you were on the accelerating body you would feel as if a pseudo force was acting upon you which caused you (the object ) to move towards the other object with a greater speed. Hence to find out the real force acting upon you you would need to have an observer in the inertial frame of reference. However where is this frame of reference?
If you think about it you yourself are not in an inertial frame of reference are you?
You are rotating on the earth and a rotating body is certainly not an inertial frame of reference as there is a pseudo force acting here as well called the centrifugal force.
So is there any point in the universe which can be called an inertial frame of reference? Scientists began looking for this stationary frame of reference and they were fixed upon ether. Ether was supposed to be a hypothetical jelly like fluid medium through which light propagates. However the michelson-morley experiment disproved the existence of ether. Hence scientists were now worried as without any fixed frame of reference they could not work out the electromagnetic theory as proposed by Maxwell for maxwell’s theory of electromagnetic waves were absolutely perfect in their description.
Now this is where einstein comes into the picture. He had been continuously thinking of how to make the electromagnetic theory work without the need of an inertial frame of reference. And then while looking at a big clock tower he finally found his eureka moment. He had been thinking if the speed of light was the same in all inertial frames and didn’t know how to make that work. That’s when it hit him that maybe time was affected in the overall process. And then he postulated his special theory of relativity.
The two postulates of his special theory of relativity are:
1) the laws of physics are the same in all inertial frames of reference.
2) the speed of light is constant in all frames of reference.
These two postulates worked perfectly as it has been measured to be found that the speed of light was truly constant in all inertial frames of reference.
Here is what this means. In our previous example we used the objects a and b. Now let us suppose that a shone a torch light towards b. Let the speed of light to an inertial frame of reference be c. Then the light beam is supposed to have reached b at a speed of c-(va-vb).
However it will be found that the speed with which the light beam still reached b is still c.
It discarded the need of an absolute inertial frame of reference and hence the notion of ether.
However it had certain consequences as well like time dilation and space contraction!
What are they?
Well here is a brief example of what it might look like.
Supposing there was an observer in the S frame which is relatively at rest to another frame and suppose there was another frame S’ which moved with a velocity v with reference to the stationary frame S.
Velocities (and speeds) do not simply add. If the observer in S measures an object moving along the x axis at velocity u, then the observer in the S′ system, a frame of reference moving at velocity v in the x direction with respect to S, will measure the object moving with velocity u’ where (from the Lorentz transformations above):
The other frame S will measure:
Notice that if the object were moving at the speed of light in the S system (i.e. u = c), then it would also be moving at the speed of light in the S′ system. Also, if both u and v are small with respect to the speed of light, we will recover the intuitive Galilean transformation of velocities
While the equations do look big and scary i will try to make it look fascinating instead. If you look at the equations a bit more carefully you will see that at speeds close to the speed of light.
From these equations you will find that even the speeds of both the frame and the object cannot exceed the speed of light.
C+C is not equal to 2C!!
Also here are some more scary equations…Bear with me!
Consider two observers O and O’ , each using their own Cartesian coordinate system to measure space and time intervals. O uses (t, x, y, z) and O ‘ uses (t’ , x’ , y’ , z’ ). Assume further that the coordinate systems are oriented so that, in 3 dimensions, the x-axis and the x’ -axis are collinear, the y-axis is parallel to the y’ -axis, and the z-axis parallel to the z’ -axis. The relative velocity between the two observers is v along the common x-axis. Also assume that the origins of both coordinate systems are the same, that is, coincident times and positions. Then?
v is the relative velocity between frames in the x-direction,
c is the speed of light, is the Lorentz factor, again for the x-direction.
Here is what these equations tell you. They tell you that if you were moving towards an object which is stationary with reference to a stationary frame of reference with a speed close to that of the speed of light, the moving object would find takes greater time to travel a certain distance than if it were measured by an observer on the fixed reference frame. Meaning?
Time slowed down for the fast moving object.
Also in the frame of reference of the moving object itself. It would find that the moving object had to travel a lesser distance than what it would have to travel as measured from the frame of reference of the stationary observer.
I have not explained the works to my readers as it would go on for pages. However I hope you understood how relativity opens up the doors to slowing down time or contracting space! Einstein wasn’t a genius for nothing! He literally opened up the door for turning something as fictional as star wars into a living reality!!