| Author |
Message |
![[Post New]](/templates/default/images/icon_minipost_new.gif) 27 Dec 2006 21:34:25 IST
|
|
|
 A ray of light is incident on a boundary between vacuum and material that (at that particular frequency) has dielectric constant ?=-1 and magnetic permeability ?=-1. (Stricly speaking, these quantities must also have imaginary parts. We will assume that they are very small.) The incidence angle is ?. What can you say about the direction of the reflected and the transmitted rays. |
|
|
|
27 Dec 2006 21:36:19 IST
|
|
|
A boat carries a wind motor of a windmill type, which drives the propeller screw. Discuss the possibility that such a boat can sail against the wind.
|
this reply: 0 points
(with 0 
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:36:49 IST
|
|
|
Estimate the height to which a person can paul-vault. Determine the cross-section of the pole.
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:37:53 IST
|
|
|
SLIDING BOX
A rectangular box leans on a frictionless wall with one corner and rests on a frictionless floor with another corner. It starts sliding down. When will the box become detached from the wall? (Assume that all the dimensions are given.)
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:39:26 IST
|
|
|
BERNOULLI PRINCIPLE
Provide a semi-QUANTITATIVE explanation of this expensive demonstration of Bernoulli principle.
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:40:02 IST
|
|
|
BOILING DROP
A drop of water landing on a 150C hot plate evaporates within few seconds. If the temperature of the plate is raised to about 200C the drop survives for about a minute. At even higher temperatures the survival time decreases with increasing temperature. Provide a semi-quantitative explanation of this phenomenon.
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:41:26 IST
|
|
|
ROTATION REDUCTION
The picture above shows a part of a mechanical contraption exhibited in the main gallery of the MIT museum. The contraption begins with a motor (on the left) turning at 212 revolutions per minute. It is connected to a sequence of N worm-gears, that can be seen in the picture. Each worm-gear pair reduces the rotation speed by a factor of 50. The axle of the last gear in the sequence is embedded in a concrete wall and cannot rotate! Assuming that each gear consists of an axle of about 10 cm in length and 1 cm in diameter, find the smallest N for which such an arrangement is possible.
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:42:02 IST
|
|
|
POLARIZABLE PAIR OF WIRES
A system consists of two very long parallel conducting circular wires touching each other of radia a (see the cross section in the picture). Find the two-dimensional polarizability of the system in the plane perpendicular to the axes of the wires. Consider the cases with electric field is parallel to the line connecting the centers of the circles (in the cross section) and perpendicular to that direction.
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:42:41 IST
|
|
|
BIRD ON A TREE
How big does a seed on the ground have to be to justify a bird in flying off a tree branch to eat it?
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:43:17 IST
|
|
|
ISOTROPIC UNIVERSE
Observer O is located in an infinite space and is bombarded by particles (shown in blue) coming from infinity and moving along straight lines in random directions. This "rain" of particles is isotropic in its directions. At large distance from the observer there is a region of scatterers S shown in red. The region contains many scatterers of the blue particles. The scatterers are not isotropic. However, their orientation is random. Can the observer O detect the presence of the region S in the space by simply observing the distribution of particles arriving at O from different directions?
Note: You may assume that the scatterers are "dilute", i.e. a particle is not scattered more than once.
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:43:55 IST
|
|
|
BALANCING PLANK
A thick plank is placed on a log of semicircular cross section. What is the thickest plank such that the plank on log has stable oscillations?
|
this reply: 5 points
(with 1
in 1 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:44:30 IST
|
|
|
FROZEN EARTH
What would happen to the magnetic field of Earth if the planet suddenly freezes? (What will be the eventual value of the magnetic field and how long will it take to get there?)
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:45:27 IST
|
|
|
NONUNIFORM ARCHIMEDES
A planet with VERY inhomogeneous mass distribution may have a very non-uniform gravitational field on its surface, and equipotential surfaces of the field will not be flat as depicted by black lines in the picture above. Consider a body of water (lake) on the surface of such a planet. Discuss flotation of bodies in such a liquid. Can you formulate a generalized Archimedes law? (As an example consider flotation of a solid sphere.)
|
this reply: 5 points
(with 1
in 1 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:45:53 IST
|
|
|
SOLAR SAILS
Consider a cosmic sail-boat moving under the influence of the pressure of sun-light at a distance from the Sun similar to that of Earth. What kind of accelerations you can expect? How do those light-pressure forces compare with the gravitational pull of the Sun?
|
this reply: 5 points
(with 1
in 1 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
27 Dec 2006 21:46:19 IST
|
|
|
THIN ICE
Why can a person run on thin ice (over a pond), but cannot stand on it?
|
|
this reply: 5 points
(with 1 </ | |
Moderation Team
![[Up]](/templates/default/images/icon_up.gif "[Up]"){kind=icon}
