Original Problems

Solution 1 : Chess OR Physics ?

by

In this blog, we will be discussing the Solution to ‘Chess OR Physics’. Before proceeding further, make sure you have gone through the problem statement

Problem Statement (Click Here)

This solution is designed for everyone, whether you are a beginner, intermediate, or Advanced. The solution has been written in a very lucid language. The reason is simple! Let’s just keep everything easy. It’s very detailed, and if you read it slowly and thoroughly, I am sure that you will get a very deep insight into the concept of the center of mass (COM). Enjoy Reading and Keep Learning

I have attached the flow charts for the respective question parts of the solution. These will help you to get a better overview of the solution. 

(Solution is attached in a PDF file after the 3 flowcharts)

Solution to Chess or Physics - There are two methods to locate the center of mass of a body, the first one being the Traditional method, and the second one is by using symmetry
Solution to Chess or Physics - Part B of the solution shows the analysis of the board and the pieces.
Solution to Chess or Physics - Part C of the solution shows the torque calculations due to White's move 1.e4

Solution to the Problem :

Here, I am attaching the PDF file for the solution to the problem. Go through it thoroughly. 

Remember that the intention behind making this problem was not just to make the solver arrive at the solution, but instead it was to make the solver appreciate the beautiful kind of symmetry that the chessboard holds!

Topics Covered :

  • Center of Mass (COM) Calculation
  • Torque Calculation (From the Rotational Motion chapter)
Download the PDF File (Click Here) Solution for Chess OR Physics _

Physics and Electronics Originals (Until Now) :

Keep Learning!

Problem 2: Bhelpuri Problem

by

Problem Statement:

(‘Bhelpuri’ refers to a street food dish made by mixing different varieties of ingredients)

A setup of thin metal pieces is constructed in a fashion similar to the function

 where [.] is GIF (Greatest Integer Function)  ……(1)

Consider only the region 0<= x <=4p, and there are large conducting plates of area ‘A’ placed at x = 5p (plate 2) and x = -p (plate 1). Given that,  A>> 6p.

Now, a small conducting ball with charge ‘+q’ and mass ‘m’ is thrown with a velocity towards the y=p graph in (1) as shown below.

Bhelpuri Problem Figure 1: A ball approaches the plate with a velocity making an angle theta with the horizontal
Figure 1: A ball approaching the plate

The collision between the metal step and the ball is perfectly inelastic in nature. The ball and the metal step are connected to a circuit as shown below :

Bhelpuri Problem Figure 2: The figure shows the complete circuit schematic
Figure 2: Circuit Schematic

(The above figure is just the electric circuit, which shows how things are connected; it doesn’t give the representation of the actual setup.) For actual setup, refer question.

Question: 

If this is the case, then what should be the magnitude of the electric field required to make the ball just cross the lower metal step (i.e., y=0)? 
(Assume no friction anywhere and consider that the metal steps don’t affect the electric field between the plates)

Solution has been uploaded. You can access the solution by clicking the button below.

Solution to Bhelpuri Problem (Click Here)

Problem 1: Chess OR Physics?

by

    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

    A chessboard with all the pieces and their respective masses given. This is a part of the Chess or Physics problem

    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 !!