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Chess OR Physics ?
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Description :
A chessboard is designed is such a way such that the White squares are made of plate having the surface mass density as σo/2 while Black squares are made of plate having surface density as σo/4. The side of square shaped chessboard is ‘8L’ (Neglect the wooden sides). The masses of the chess pieces are given in the tabular form below.
(The notations on the chessboard can be observed from the figure below.)
Answer the question parts accordingly
Question Parts :
- Part – (a) Find the center of mass of the designed chessboard. The board is to be supported with the help of a knife edge. Also find the reaction force which will be applied between the knife edge and the chessboard.
- Part – (b) All the pieces are arranged ‘as usual’ on the board ‘simultaneously black and white pieces both’. Will it make the chessboard to get disturbed from its equilibrium? If yes then how? And if not, then why?
- Part – (c) Having set up everything, player A (white) & player B (black) are ready to start the game. If white makes his first move as 1. e4, then what option(s) does black have for making his move immediately so that the equilibrium of the chessboard is not disturbed at all ?
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Can you name the opening after both the players are finished making their first moves ?
(Completely optional)
My Expectations from the Solver :
The main intention of me behind designing the problem is to make the solvers understand the beauty of chessboard i.e. to understand how symmetrically are the pieces kept and also the symmetry of the design of chessboard. Solving a problem and getting an answer is one thing and understanding it is another. This point will surely become clear when I will post the solution of this problem. I hope you enjoy the “process” while solving the problem !!
