Class 12 physics question bank

Download an excellent collection of questions with answers for CBSE Class 12 Physics

Question Bank in Physics Class XII

The collection will also be helpful for students of other syllabuses.



The file consists of syllabus, key points, collection of very short Answer (1 mark), Short answer type question - solved (2 marks), short answers (3 marks), Long answers (5 marks), Solved numericals and 3 sample papers.

The contents are arranged chapter-wise. Any student will find this a boon for easy preparation and to score better marks in Physics.

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Alternating Current and Direct Current

AC/DC (electricity)

Electricity is the most widely used form on energy because it is most efficiently distributed and transported. Also it can be easily converted to other forms of energy like mechanical energy, heat energy etc. Also since it is one of the fastest forms of usable energy it is used in logic digital circuits for computation since it gives the fastest results. It is this versatility of electricity that makes it so useful for modern life.
Of course electrical energy has various forms as well. It can be stored charge, alternating current or direct current. Each of these forms of energy have different advantages. Now we know that most  of power that we get in our homes is in the form of AC. However it is not necessarily the most used form of energy. In fact most electronic equipment use DC power and converts AC from the supply to DC. Then why is it made AC in the first place. Let us discuss that shall we?

Inside a Car Engine

(Internal Combustion Engine)

We cannot imagine modern life without the car. The automobile has been one of the singular most amazing inventions of the 21st century and almost defines modern times. Inside of most mechanical petroleum based vehicles is the internal combustion engine.
Today we shall have a brief look at the internal combustion engine and it’s basic working principles.
Basically the the internal combustion engine is a cyclic machine that works on the basis of polytropic expansion laws.
polywhat?!

Ok so a polytropic process is one in which the gas equations work differently than that stated in boyle’s law because temperatures need to be constant for the famous law to work. (Pressure*Volume= constant at constant temperature)
Here since during expansion of the gases the temperature does not remain constant and hence the law looks like:
Pressure*Volumex =constant

The variable x depends upon the gas used.

So as you can see pressure will have to change greatly for the equivalent volume to change and to keep the equation valid. That’s exactly what happens in an internal combustion engine where an small explosion changes the pressure greatly but the limited volume is not much and hence the equivalent change in volume remains small.


First cycle: Suction
As you can see from the diagram the camshaft being slightly oval is rotating about a central point which for a certain time pushes the lever which opens the valve connecting the gasoline tank to the combustion chamber. The engine is so tuned such that when the fuel flows from the gasoline tank to the combustion chamber the bigger rotating structure downwards pulls the piston downwards. Hence the fuel gets trapped in the chamber when the valve closes.

Second cycle:Compression
This is the part where things get interesting. With the fuel trapped inside the chamber due to valve action the wheel rotates such that it pushes the piston above and compresses the fuel. This fuel now now has to withstand high pressure as the piston has lowered the volume greatly. When it is compressed at the maximum a spark plus in the chamber is ignited which causes a small explosion to increase pressure rapidly and push the piston downwards.[remember the part where i told you that the volume is quite limited but the change in pressure is enormous]

Third cycle: Expansion
Here work is obtained from the engine as it causes the rotation in the rotating part attached to the piston to increase. The expansion is the part where the actual energy is obtained from the engine. The wheel continues to rotate by inertia. This is why sometime you need to move the car a bit before getting it to work. It is because the first two parts of the cycle need energy to function and it’s the third cycle which actually provides work.

Fourth cycle: Exhaust
Now the second camshaft is made to rotate at such a speed that by the end of the third cycle  the exhaust valve opens up and the fumes that remain after the explosion is forced out by the upward movement of the piston.
Now the second cycle starts where the piston is made to move by inertia and hence the cycle continues.


That’s it! That’s how the internal combustion engine works. Now obviously you will not get an exact replica of this engine inside your car. Rather they have as many as four piston moving up and down to form a 4-stroke internal combustion engine. Also they have a variety of cooling mechanisms and noise filters to reduce the noise from the explosion that takes place inside the machine. However this is the absolute basic and all other made upon this model. There are differences between a petrol and a diesel engine but then again they are not much different from this model.
So now the looking up the car engine  won't seem like an engineering job at NASA anymore, would it?!

Hydrogen Economy

 

As the world’s fossil fuels are continuously depleted with increasing use we run the risk of facing a shortage soon enough in the future.  Alternatives are a must as we already face the heat here in India with capping of LPG cylinders. One of the biggest consumers of fossil fuels are petroleum-based vehicles. Whether it is a diesel car or a petrol car or a CNG vehicle it doesn't really matter. They all use fossil fuels which are bound to run out one day or the other. We need to continuously improve current efficiencies of transportation vehicles while still improving on alternative energy sources. One of the biggest solutions to alternative energy solutions are using hydrogen instead of carbon based fuel as an energy source.



 

Hydrogen as a fuel has a lot of potential to be used as energy because it not only releases a large amount of energy when burnt but it also prevents the release of toxic fumes as pollutants.

Let’s do a little bit of math shall we?

I promise it won't be too large.

 

 

Bond energies of hydrogen

 

The bond energy of the hydrogen bond is 103 kcal/mole. And the bond energy of the hydrogen oxygen bond is 110 kcal/mole. Also the oxygen molecule has 116 kcal/mole of energy.

Therefore the energy released on formation of the water molecule requires breaking one oxygen molecule and two hydrogen molecules first.

 

That would mean the energy required = 2 x 103 + 116 = 322 kcal/mole

 

But when water is formed the energy released is = 4 x 110 = 440 kcal/mole

 

Hence the net energy gain = 440 - 322 = 118 kcal/mole

 

And this simple math shows the huge amount of energy which is gained on burning hydrogen as a fuel. If a human being were to be powered up by a hydrogen engine he would run 52 miles on just 1 litre! Hydrogen based cars can theoretically provide mileage as good as 93 miles per gallon which is still much better than gasoline based cars providing 35 miles per gallon.

 

Yes and that’s exactly why hydrogen is a potential energy alternative.



 

This picture shows exactly what the components of the hydrogen economy consist of.I won't talk about all the boring points in detail but only some of the parts which are really interesting.

 

Production and delivery

Hydrogen has a huge source in the form of our vast oceans and seas which provide an ample source of hydrogen. The problem is converting the water to hydrogen which requires energy in the first place.

 

Well right now they use natural gas and other petroleum products as well as biogas to produce hydrogen. Yes production is actually the biggest hurdle to the hydrogen economy. Hydrogen requires huge amounts of energy to be produced.(It only makes sense since it produces a huge amount of energy on combustion as well.) People are actively working on getting hydrogen to be obtained from a safe source. There are many technologies like aluminium based production (still waiting to be patented) for effective hydrogen production.

And yes there are several hoaxes doing the rounds around the internet which claim to have made super efficient methods to obtain hydrogen from water and hence make cars that run miles on just plain water!!! Well NASA itself has yet to make such a breakthrough but of course there is no giving up hope as people are still trying.

 

Although I am optimistic that this  can be effectively taken care of using solar , wind , hydel power and various other renewable energy sources(like i told you before the future depends on all energy renewables working together) Then the hydrogen can be transported using storage tanks to fuel stations where the vehicles can refill their tanks!

And no I am not talking about science fiction. This is reality as industries work to implement these systems into the current economy.

 

Fuel cells

This is the talk of the town when it comes to hydrogen based economy. Fuel cells use a continuous supply of hydrogen to be directly converted to energy using a chemical reaction. This means efficiencies are quite high when using a fuel cell to power up a vehicle as compared to using internal combustion engines to power up a car.

There is huge money in the R&D for fuel cells in the automobile sector.There have been lots of hydrogen based fuel cells which are running commercially as well. Although there has been electric vehicles which have been shown to have much higher efficiencies they lack the power or speed pick up of fuel cell based cars and car maniacs out there swear by top speeds and revving pick up.



Storage

Now this is a real tricky issue hydrogen is the lightest of all elements out there and it is easily the least dense of all gases. In fact 1 gram of hydrogen would occupy as much as 22.4 litres! that too at 0 degrees celsius. Not too good when considering that we would need more than that to provide decent mileage to the vehicles. Well scientists have been looking for ways to combat this dilemma.

 

One of the ways include in-situ production of hydrogen.

It means the hydrogen would not be carried directly as a fuel. Instead hydrogen containing compounds would be used to generate the hydrogen at the time of running the car. However this method reduces efficiency significantly and renders the use of the vehicle as useless!

 

Another one of the methods include storage of hydrogen in a really efficient way

This means nanotechnology again! Yes the use of carbon nanotubes to store hydrogen has been deemed a potentially powerful method to store huge quantities of hydrogen in the vehicles. That however is a costly method and current research includes making hydrogen storage even cheaper.

 

 

Safety?

Now this is a bit of a tricky issue because hydrogen is even more susceptible to combustion than petroleum. Although that also means that fires breaking out won’t produce toxic fumes but then again they will bring out a bigger bang if they accidentally catch fire. Also current hydrogen storage techniques are not exactly 100% leak proof which means the dangers of accidents are higher! However this can be offset by using standards and protocols to enhance the safety factor of using hydrogen.

 

So what’s the real problem in implementation of hydrogen as a potential energy source?

Well this again lies in costs. Changing equipment and technology that has been built on petroleum will cost huge amounts and also current petroleum-based vehicles and fuel rates are cheaper than those of hydrogen based ones. Of course this should rapidly change in the very close future. In fact there are many companies already that provide hydrogen cars and hydrogen refuelling outlets.




Yes these are real hydrogen cars in the market out there.

 

Ocean Energy

Ocean energy
Now renewable energy sources come in various forms and make great pollution alternatives to coal and other exhaustive resources. Now scientists have been looking for all sorts of alternatives and creativity is often more valued than analytical solutions. Our great oceans store vast amounts of energy in the form of heat(anyone remember that water has the highest specific heat capacity?) mechanical (think thousands of gallons of moving water and the momentum it possesses!) as well as chemical energy (water has a lot of energy in those bonds between hydrogen and oxygen).

Some forms of utilizing tidal energy

1) Wave energy

Here the moving energy of waves is utilized. As can be seen from the figure the moving energy of the waves forces air out of the turbine when it is moving up and forcing air into the turbine when it is moving down. Hence this movement of air can be used to turn turbines . It creates a small source of power but nevertheless it is used in coastal areas for powering small lighthouses and other small electrical equipment.
Sometimes the motion of the wave itself can be used to power a piston to move up and down which in turn can turn a generator.

2)Tidal Energy
Tidal energy is the real current practical source of energy. It uses the tides to store water during high tide and then during low tide the water is released just like a hydroelectric power dam. It’s really simple but the problem is that the tides need to rise really high in order to make it work effectively.
However India’s own coastal lines are quite suitable for this sort of energy and some our IITs are working on making tidal energy a viable source of energy to provide the coastal needs of power.

3) Ocean thermal energy

There is a vast difference in the temperatures of the surface of the ocean and the bottom of the ocean. This temperature difference itself can be used to produce electricity.
Now normally one would assume this electricity produced to be of very poor voltage.(In the seebeck effect about 500 degrees celsius produces about 500 mV).
Hence it has not gained much popularity as an alternative energy source.

New research
Now don’t be so quick to cutting out Ocean Thermal Energy Conversion(OTEC). Ocean thermal energy can be used to generate electricity in new ways it seems again thanks to the potential boundless limits of nanotechnology. It seems scientists have found new ways to harness the heat to generate electricity.

Over time if this new technology could be developed to harness the temperature difference between the surface of the ocean and it’s bottom there could be potentially boundless limits since it could also use the temperatures found in factories, automobiles, deserts(think of deserts as giant energy batteries or so that’s what i think.)
Another interesting phenomenon about tidal energy is that it is not a solar based energy source(most of our energy sources are solar based directly or indirectly) but it is actually based on the lunar force of attraction. So it seems that using the moon as a potential energy source is by itself quite an innovative idea...don’t you think?

History Of Gravity

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!

Related articles

• Relatively relative

Solar Energy And The Optimistic Approach

So we have been talking about all the various problems of solar energy. And I am sorry to start it off with such a negative note but I did it because I wanted to end it on a positive note.
Yes , that’s right, solar energy holds a lot of potential And it “IS DEFINITELY” the future of our energy needs.

So why is everyone so optimistic on solar energy?
It’s simple. Because ever since life began on earth nature has always depended on solar energy for it’s continuous energy needs and evolution. Even the fossil fuels we use are indirect products of solar energy. The solar energy provided the animals and plants with energy as we know by photosynthesis and the food chain. These plants and animals died and their remains were buried under pressure and heat to form coal and petroleum as we know today.

So it’s obvious that solar energy should be our natural choice to be looking for. In fact Thomas Edison said that solar energy was the most natural as well as the most abundant source of energy available for us. Hence it is imperative that we try to find ways to harness it as much as possible.
So what’s the solution?
Simple!
Never give up!

That’s right scientists are striving today to make solar energy as much viable as possible and I have good news for you!!! Solar energy has made quantum leaps and it is proving to be a boon for many cities with abundant sunlight. Even during the night!

Here are some of the problems which are being tackled about solar energy.

Efficiency
The biggest drawback to efficiency is costs . Well scientists have been working on just those lines and they really have managed to increases efficiency and reduce costs as well. Yes they have developed new techniques and methods to greatly enhance consumer level use. It won’t be long before you will see everyone changing their power supplies just like how everyone is going digital from cable TV.

How?

1) Quantum dots
The solar PV cells are made even more tiny so that a greater surface area is exposed to the solar radiation resulting in good efficiencies.Nanotechnology holds huge promise in energy harnessing storage, as well as other industrial needs and the energy companies are no exception. And the best part is there has been steady progress in using quantum dot PV cells.


2) Splitting the solar spectrum
Solar PV cells use only a part of the solar spectrum to produce usable energy. The remaining part is lost as heat. This heat can actually reduce the efficiency of the system. Now given how summers can be blazing hot in India especially. We wouldn’t want a power supply that runs on solar power and yet gets fried with excess heat.

Now this is where material scientists(the broader group under which falls the nanotechnology scientists) play their part in making the cells more heat resistant and usable under heat. A new technology uses a material such that it emits only those wavelengths which are harnessed by the cells to produce energy.

Some people have even used the simple fibre optics which was originally used in communications. But since it characterises no loss transmission it is also a pioneer in using correct frequencies.

3)Concentration cells
Concentration cells uses parabolic reflectors to focus the sunlight onto a small area of the PV cells which is found to increase efficiencies amazingly. Photoelectric emissions which requires greater frequency to produce electrons of good kinetic energy, while  photoelectricity requires greater intensity of sunlight to produce more electricity.

Hence we have a reduction in costs with materials used and we get more usable energy from the same amount of solar radiation. So it’s a pretty neat technique.

But what about the production of energy during the night and what about cloudy and rainy seasons?
Again I have good news as researchers have found more and more efficient ways to store solar energy during the night time as well. A new method that they have developed is using lots of reflectors to focus the radiation onto a tower. That tower contains a form of salt and the solar heat melts that salt to a molten state. This molten state dissipates heat very slowly and it is kept in as much thermal insulation as possible. During the night the heat from this molten salt is used to power up homes during the night!! In fact it can well last for 8 to 10 hours for commercial needs of a locality. Not bad for a salt based system!

As for the seasonal changes that’s where the limitations come in. But researchers are still working on high altitude solar panels and increased efficiency panels. In fact here again fibre optics plays an optimistic role in transferring energy from high altitudes. However it won’t be enough for commercial energy needs and this is where the other renewable sources come to play like hydel energy, wind energy.

In fact if you think about it carefully summer is the time when there is no wind or rain and solar panels would rule. But the other seasons are sufficiently more windy and rainy which means that wind and hydel power would be a boost. So the various renewable energy sources complement each other.

After reading about so many new revolutionary inventions and techniques the world doesn’t seem so bleak due to the global warming catastrophe anymore does it? However that does not give us reason to continue our wasteful ways. We must continue working on sustainable development so that our future generations continue to reap the benefits of nature and keep the human race moving forward.

Solar Energy

I am sure solar energy requires no introduction. Today India is being rocked by issues like the Nuclear proliferation treaty, coal scam etc. These are primarily because of the impending energy crisis that the world will come face to face with soon enough. And India is going to be one of the worst affected as it is one of the most densely populated countries. We recently got a glimpse of what might happen when fossil fuels get exhausted when there was a massive grid failure in the northern parts of the country. It was because of the fact that some of the states drew more than excess power that caused the generators to slow down thus disrupting the entire grid. It exposed the country’s dependence on fossil fuels only and the impending need to promote renewable energy sources. Sadly our policy makers are not too concerned with tapping alternative energy sources while all efforts to do so(nuclear power) is met with opposition for petty politics.
However there are plenty of other sources as well. While hydel power is a prospective source of energy in India it is consequential because it can damage fragile ecosystems and displace entire populations. Then naturally Solar energy seems to be the logical choice.
So what’s stopping them from adopting solar energy?
Two things:
a) Cost
b) Erratic supply
a) Cost
Yes like any other new product in the market costs determine how effectively it can be implemented. The biggest problem with solar energy is that it is very expensive. Yes it takes about 2000$ just to install solar Photovoltaic(PV) modules plus even in the well developed sunny states of the U.S. the cost of solar cells is about 0.11$ / kWh. Now that really is expensive if you compare it in the Indian currency.
b) Erratic supply
Yes it is true that India has a huge amount of solar radiation input being in the tropics and everything working out to be fine India should be having more than enough energy to compensate for the energy needs of the country. BUT we should also try to remember that India is a place where the monsoons cover the Indian skies with clouds for a considerable part of the year too. This does deter the energy supply and this would have been a cause of great distress among the millions as energy demands are high and an uninterrupted supply is necessary in many parts of the country. Plus supply during the night time would be a huge problem as there is no effective way to store energy obtained during the day.
But what exactly is  a photovoltaic cell?
A photovoltaic cell uses photons from the sun’s energy spectrum and converts it into kinetic energy of electrons.

It has an antireflective coating at the top to remove any sort to prevent loss of solar energy by reflection. As can be seen from the diagram, The photons strike the electrons at the junction of the p type and n type semiconductors to create a voltage difference. This voltage causes a current to flow in the closed circuit.
If solar energy needs no investment other than maintenance to continue then why should the initial high cost be a problem?
Well the problem comes from the fact that efficiency of solar PV cells is very small. Typical energy efficiencies are about 8 to 10% today. In fact all the major corporations of the world are working on increasing efficiencies as you read this article.

As you can see the technology used increases efficiency a lot. But what is not mentioned here is that the cost of increasingly complex technology is quite high. Efficiency determines the fate of new technology as solar pv cells are no exception.
But that does not mean that solar energy does not hold promise. For it has been calculated that the amount of solar radiation the earth receives at the sea level is more than enough to supply 8 times the energy requirements of the World’s population.

Relatively relative

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

phew!!!

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?
where:

• 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!!

Career Prospects in the field of Statistics and Economics

What are career prospects in the field of Statistics and Economics?


Economics being a social science is considered to be very vital in analyzing the effects of production, sales including consumption of goods on the economy of the user or the common man. The concept of economics is applied in every field; be it an industry, agricultural sector, banking sector, labor sector the principles of economics has a dominant role to play. In fact many of the leading industries including banks engage the services of economists to advise the industry or the organization on many of the policy matters including those involving production and matters relating to financial propriety and a host of other relevant issues. Every government will engage the services of economists to advise the government on various issues concerning the government policies on price control, banking regulation and such other related matters.

Those who aspire to take up economics as a career have the option to take up diploma course in economics. However, from the career prospects the diploma course may not be much feasible. Therefore, it is advisable that they take either graduate or postgraduate course in economics. As already mentioned in economics there are several areas of specialization like for example agricultural economics, industrial economics etc. Therefore depending on the specialization the career can be preferred. Remember, your opinion as an economic adviser has great value in terms of forming the future policies of the organization. Therefore it is a very prestigious and equally a responsible position.



A statistician is the person who works out with the data available all around us and as one expert puts it he ‘churns out’ the result. With his innovative approach and scientific principles he draws conclusions to various issues and it forms the basis for your policy making and plan future course of action. Every organization and particularly industries and the government need statistical data to regulate their work and also take effective policy decisions. Similar to economics, the curriculum in statistics consists of diploma, bachelor as also post-graduate courses. However in order to have promising career, it is advisable to complete either the graduate or post-graduate course with specialization.

According to experts, similar to economists, the carrier as statistician is very much promising. Considering the impact of statistical analysis on the future policies of the organization the position of statistician is considered to be very much important and it is one of the highly regarded positions. Normally, statisticians are appointed as consultants. However, some of the organizations and particularly the government would appoint them on a permanent basis or at least on a contractual obligation for certain period of time. Agriculture, industry and banking sector need the assistance of statisticians on a regular basis. It is also said that some of the educational institutions also require statisticians on teaching assignment. Those who have aptitude for teaching can look for these positions.  In fact some of the experienced statisticians even establish their own consultancy services where they even coordinate with experienced economists so that the client would get both the services in one roof.