Problem Description:
A chessboard is designed in such a way that the White squares are made of a plate having the surface mass density as σo/2, while Black squares are made of a plate having surface density as σo/4. The side of the 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. I’ve also attached 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 disturb 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) and 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?
*Can you name the opening after both players are finished making their first moves? (Completely optional)
My Expectations from the Solver :
The main intention behind my design of the problem is to make the solvers understand the beauty of the chessboard, i.e., to understand how symmetrically the pieces are kept and also the symmetry of the design of the chessboard. Solving a problem and getting an answer is one thing, and understanding it is another. This point will surely become clear when I post the solution to this problem. I hope you enjoy the “process” while solving the problem !!
Solution has been uploaded. You can check it out with the link below.
SOLUTION
Enjoy Solving !!
