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![[Post New]](/templates/default/images/icon_minipost_new.gif) 27 Dec 2006 22:00:36 IST
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DELICATE BALANCE
Consider a lead pencil balanced on its point. Estimate how long it will remain standing if quantum effects (uncertainty principle) are taken into account. Compare that answer with the time it takes for thermal effects (air molecules, thermal radiation (if it's in vacuum)) to topple it.
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27 Dec 2006 22:01:02 IST
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THREE-SIDED COIN
What should be the dimensions of a coin that has probability of 1/3 to fall on its obverse ("heads") side, 1/3 - on its reverse ("tails") side, and 1/3 - on its edge.
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27 Dec 2006 22:01:27 IST
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IMMORTAL BACTERIA
Bacteria are almost immortal. (Apollo 12 crew recovered bacteria that were accidentally brought to the Moon 3 years earlier by Surveyor probe, and those bacteria were revived. There are claims of revival of 30 million year-old bacteria.) How long will it take for the cosmic radiation to destroy the DNA of a bacterium.
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27 Dec 2006 22:01:52 IST
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THREE-PHASE CURRENTS
Why do power companies produce three-phase currents. What are the advantages over single-phase, two-phase, four-phase,... currents?
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27 Dec 2006 22:02:27 IST
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EQUIPOTENTIAL SURFACES
Let the equation
F(x,y,z)=c
represent a set of nonintersecting surfaces. (Each c corresponds to a different surface.) What is the condition that this is a set of equipotential surfaces? In other words, can we define such potential V(c) that its Laplacian vanishes?
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27 Dec 2006 22:02:50 IST
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MAXIMAL GRAVITY
Consider a celestial body (planet) of mass M and volume V consisting of material of uniform density M/V. If the body is spherical, then its radius is R=(3V/4{pi})1/3, and the free-fall acceleration on its surface is g=GM/R2=GM(4{pi}/3V)2/3, where G is the gravitational constant. Consider all possible shapes of the body. What is the largest g, that can be achieved at one point on a surface, and what is the shape of the body for which such acceleration is achieved?
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27 Dec 2006 22:03:24 IST
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SOAP BUBBLE
Calculate the time of disappearance of a soap bubble connected with the atmosphere via a capillary.
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27 Dec 2006 22:03:52 IST
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SCATTERING DIPOLES
A system consists of two ideal dipoles placed at positions (0,0,0) and (0,0,a). Dipole moment p of each dipole is related to electric field E on that dipole via relation p=gE. (g is so small that you can neglect the interaction between the dipoles, i.e. electric field created by one dipole at the position of the other dipole is negligible.) An incoming electromagnetic wave of wavelength L=2a is scattered by the system. Consider two cases: (a) the incoming wave is in x-direction, and (b) the incoming wave is in z-direction. Estimate the ratio between the total scattering cross sections between those two cases. (You may neglect dimensionless prefactors of order unity.)
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27 Dec 2006 22:04:24 IST
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LINE OF CHARGES
Consider N identical "charges" placed along a straight line. A pair of charges at positions xi and xj repel each other via potential -ln|xi-xj|. Each charge is attracted to the origin of coordinates by a parabolic potential xi2/2. Show that the equilibrium positions of the charges are given by the zeroes of the Hermite polynomial HN.
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27 Dec 2006 22:05:23 IST
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ISOTROPIC RADIATOR
Is it possible to build and antenna that will radiate coherent electromagnetic radiation with intensity independent of direction?
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27 Dec 2006 22:06:06 IST
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CURRENT IN A WIRE
In freshman physics we are told that a current in an "infinite" cylindrical wire flows with constant density J independent of this distance from the center of the wire. But we also learn how to use Ampere's Law to calculate the magnetic field in the wire. Doesn't the magnetic field act to make the current density non-uniform?
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27 Dec 2006 22:06:25 IST
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CURRENT IN A WIRE
In freshman physics we are told that a current in an "infinite" cylindrical wire flows with constant density J independent of this distance from the center of the wire. But we also learn how to use Ampere's Law to calculate the magnetic field in the wire. Doesn't the magnetic field act to make the current density non-uniform?
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27 Dec 2006 23:14:51 IST
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that are so many questions!!!!
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Njoy!!!!!! |
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28 Dec 2006 01:12:09 IST
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also more than 4-5 new questions a day from the same user will fall back in the query queue for experts. also please dont copy paste entire question papers from other locations on the community. do remove all these posts by yourself (else they'll be deleted soon) and share the liks with your community mates if you want to. It will be great for them too. cheers ~admin
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God is real, unless declared as Integer!!
Congrats to the crackers... All the best for re-trials (it takes more courage and u guys deserve a lot more accolades) .. cheers!
Welcome our latest moderators magiclko , greatdreams , spideyunlimited and bhupesh |
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28 Dec 2006 19:24:43 IST
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Moderation Team
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