[As usual, div(interesting physics questions) has a singularity near Mojan :-) ]

1. A ball is thrown up into the air with some velocity. What distance does it travel in the last second of its ascent?
(This is a quickie, you should solve it (in < 10s :)) without writing down anything, and without substituting for any formula in your mind. Yes, there _is_ a nice way to do it.)

2. We've all heard that Earth takes 23 hrs 56 minutes to rotate once around its axis, not 24 hrs. Then, if today the Sun rises at 6:00 AM, tomorrow it should rise at 5:56 AM, ie 23 hrs 56 minutes on the clock. Soon, we'll have the sun rising at 1 AM ! Why doesn't this happen ?  ¶ 10:21 AM 6 Comments

  1. The average heat energy input on a 1m^2 solar collector around mid-day is about 1000W. Now, suppose I have a VERY large (parabolic) solar collector. Suppose I now send in a very small amount of water near the focus. It is going to get heated up. If I fix the size of the collector and the amount of water I send, I can get the temperature of the water to go above 6000 deg C, the avg temperature of the surface sun. But if you observe closely, this is in violation of the second law of thermodynamics, because we just transferred heat from a colder body (the surface of the sun) to a hotter body (the water). Now where exactly did we violate physics?

(Water is only an example working fluid, it might have been anything else)

2. F(z) = Fourier Transform(f(t))
What is the Fourier Transform of F(z) ?

3. A lift car has a pulley (call it pulley A)hanging from its roof. There is a rope passing on pulley A, and on one side of the rope, a 2kg mass is hung, and on the other side, a 3kg mass.
Now, the entire lift car is hung by a second rope, which passes over a second puller (call it pulley B), and there is a 5kg mass on the other side of pulley B.
The mass of the lift car is negligible.
Will the lift car move ?

Hint: (rot13) Jul pna lbh abg pbafvqre gur yvsg pne gb or n 'oynpxobk' jrvtuvat 5xt ?  ¶ 11:01 AM 9 Comments

  ( Q1 and Q2 courtesy Vimal. Thanks!)

1. Why do you always see extensions of tar.bz2 or tar.gz in linux ? tar simply aggregates all files into one big file (a 'tarball'), and gzip or (bzip) does the actual compression. Why is it better to tar something, and then compress it, instead of, say, the other way round?

2. Some compression programs allow you to encrypt a compressed file. If you were the designer of such a program, would you choose to encrypt after you compress, or compress after you encrypt?

3. 200 random integers are displayed on a loong board, one beside another. There are two people, A and B. The game starts like this: player A chooses a number, either the leftmost (1st) or the rightmost (the 200th). Player B then chooses the leftmost or rightmost number among the ones available. (ie, if A chose the 1st, B can choose either 2nd or 200th, or if A choose the 200th, B can choose either the 1st or 199th). The game ends when all numbers are exhausted. The player with the higher sum of number wins. If you are A, what would you do to make _sure_ you will win always ?

4. There is a circular table of radius R, and a very large number of circular coins of radius r (R > r). Two players, A and B. A begins by placing a coin somewhere on the table. B then places a coin somewhere. The game ends when either of the players is unable to place a coin (ie., the table is full). If you are A, how would you place your coins to make sure you will win always?  ¶ 10:49 AM 1 Comments

  1. A number consists of 100 Zeros, 100 Ones and 100 Twos in a random order. Is it a perfect square?

2. Given a set of random numbers a1,a2..aN, find an algo that finds the maximum and minimum in ((3n/2) - 2) steps.

3. Topcoder factorial problem. http://www.topcoder.com/stat?c=problem_statement&pm=6398&rd=10000  ¶ 9:16 AM 2 Comments

  main()
{
int a[3] = {0,1,2};
b = a[2];
c = 2[a];
}

It is possible to write a makefile such that b and c are taken to be implied types.

What are values b and c ?  ¶ 12:21 PM 0 Comments

  Your keyboard generally has between 105 and 120 keys. The number of pins in its PS-2 (or USB) cable is generally 6. The keyboard is a digital device. 2 ^ 6 = 64. How come 105 keys can be used then?

(No, there is not '64 subset' active at any point of time. All 105 keys can be pressed, and their states can be perfectly displayed by a simple C program)  ¶ 12:16 PM 1 Comments

  1. You have water in a burette. You note down the level of water. You drop a block of ice in it, and then note down the level L0. After some time, all the ice melts. Now the level you note is L1. What is L0 - L1 ?

2. You have a spring balance that can measure a maximum of 50 kgs. You need to measure a component whose weight is about 75-90 kgs. How do you do it?

3. You have a standard,small cylinder-shaped weighing guage. Given nothing else, find its weight.  ¶ 11:00 AM 2 Comments