IIT JEE , AIEEE Forum - Physics , Mechanics

sravan

Two identical light bulbs are arranged in a circuit with a battery, and a switch S, as shown.

When the switch is closed, the brightness of bulb A ...

sravan

Two identical light bulbs are arranged in a circuit with a battery, and a switch S, as shown.

When the switch is closed, the brightness of bulb B ...

sravan

Click on the questions for the answers

FOLLOW-UP: What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy?

Periodically I hear stories about ball lightning. Does this phenomenon really exist? Could a ball of plasma remain stable for several seconds, as some researchers have claimed?

I have been arguing with a friend of mine about car crashes. If you were going to be in a collision, would it be "safer" to hit a tree or a power pole than to hit an oncoming car head-on? I always thought the tree or power pole, because they give. If you were to hit another car head-on it would be twice as bad because it is your speed plus theirs when you collide. My friend believes you are better off hitting the on-coming car. Who is correct?

What exactly is the physical or chemical process that makes adhesive tape sticky?

sravan

Can any body give answers for the first ones?

sravan

If you examine a modern parachute you will notice that it has a large hole at the top. Why is there a hole in the parachute?

sravan

A not-so-famous athletics coach once said that ?Because of the rotation of the Earth, an object can be thrown further if it is thrown to the west.?

Using your Preliminary Course knowledge of vectors, determine whether this statement is an accurate description of the real world? Explain.

DATA: The Earth spins on its own axis from west to east at about 1833 km/h at the equator. An average, red-blooded Australian can throw a cricket ball at about 100 km/h, if he/she really wants to. Giant cephalopods are quite dangerous and are to be avoided at all costs.

sravan

Most aspiring Physicists on planet Earth would recognize the command "Beam me up Scotty". Star Trek's famous "transporter" could deconstruct people into their sub-atomic essences, send that information over a given distance and then reconstruct the people from that information at their destination. What a great way to travel!

Those of you who are studying the "From Quanta To Quarks" Option will come across the work of Werner Heisenberg, notably the Uncertainty Principle. How might this principle impact on the possibility of a Star-Trek-type transporter?

Have you heard of quantum entanglement? How might this phenomenon enable Physicists to achieve quantum teleportation?

sravan

The Greek mathematician Diophantus is generally regarded as the "Father of Algebra". Diophantus first used algebraic notation and symbols around 250 AD. He wrote a treatise on algebra in his "Arithmetica", comprising 13 books. Only six of these books have survived.

A mathematician to the very end, Diophantus' age can be determined from the epitaph on his tombstone. An English paraphrase of this epitaph reads:

"Diophantus passed one-sixth of his life in childhood, one-twelfth in youth, one-seventh more as a bachelor; five years after his marriage a son was born who died four years before his father at half his father's final age."

How old was Diophantus when he died?

sravan

Imagine you are at a party with 22 other people. What is the probability that any two of the 23 people at the party will share the same birthday? Assume 365 days in the year.

sravan

So, you think you are pretty good at Chemistry eh? Well try this little sizzler.

The solubility product of MCO3 in water is 25 times as great as the solubility product of MC2O4 in water at the same temperature. A mixture of K2CO3 and K2C2O4 totalling 2.042 x 10-3 mole was dissolved in water. To this solution was added 2.80 x 10-3 mole of MCl2. Water was then added to give a total volume of one litre. When precipitation was complete a mixture of MCO3 and MC2O4 totalling 2.000 x 10-3 mole had precipitated. Calculate the solubility product for MC2O4.

Note: In case you are ranting and raving that this is just too hard and is obviously university standard ? think again. This was question 2 from the HSC First Level Chemistry Exam back in 1974. Dear me, how standards have changed.

sravan

Complex numbers (imaginary numbers) are numbers of the form:

a + ib, where a and b are real numbers and i is

the square root of minus one.

Not only are complex numbers extremely useful in the subject of mathematics, they play an essential role in many areas of Physics - Electromagnetic Theory, Electronics, AC Circuit Theory, Atomic & Nuclear Physics, Quantum Physics, Wave Theory and Signal Analysis just to name a few. In many situations in Physics, the real solutions to a problem would be inaccessible without the use of complex numbers. For instance, Schrodinger's Equation, the basic equation of wave mechanics expressing the behaviour of a particle moving in a field of force, contains the imaginary number i (see below).

The following little exercise is probably best attempted by Extension 2 Maths students after learning about complex numbers.

The polar form of any complex number w can be written as:

w = r eⁱ^q

The circle with r = 1 is called the unit circle in the complex plane. All complex numbers lying on this circle are of the form:

w = eⁱ^q , for q real.

Using the Cotes-Euler formula

eⁱ^q = cosq + i sinq for real q.

This equation encapsulates the essentials of trigonometry in the much simpler properties of complex exponential functions. Use this equation to show that:

cos(A + B) = cosAcosB - sinAsinB

sin(A + B) = sinAcosB + cosAsinB

cos3q = 4cos³q - 3cosq

sin3q = 3sinq - 4sin³q

sravan

On June 7 of 1935, Erwin Schrodinger wrote to Albert Einstein to congratulate him on what is now known as the EPR paper, a famous problem in the interpretation of Quantum Mechanics. Soon thereafter, he published what was to become one of the most celebrated paradoxes in quantum theory:

Schrodinger's Cat

A cat is placed in a box, together with a radioactive atom. If the atom decays, and the geiger counter detects an alpha particle, the hammer hits a flask of prussic acid (HCN), killing the cat. The paradox lies in the clever coupling of quantum and classical domains. Before the observer opens the box, the cat's fate is tied to the wave function of the atom, which is itself in a superposition of decayed and undecayed states. Thus, said Schrodinger, the cat must itself be in a superposition of dead and alive states before the observer opens the box, "observes" the cat, and "collapses" its wave function. In other words, before the observer opens the box and observes the cat, the cat is BOTH dead AND alive at the same time. Cute, eh? What are your thoughts on the matter?

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