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Solution 3 : Smartwork > Hardwork

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Have a look at the problem once again if needed : QUESTION 

Here we have the Solution to the problem : Smartwork > Hardwork !!

The level of the problem is EASY in comparison to the previous 2 problems (Chess OR Physics?   &    Bhelpuri Problem). The problem is mainly based on Electrostatics 

  • The problem gets it’s name based on the approach you choose to solve the problem & get the answer. The thing which I want to tell from my side is that, Try to read the problem carefully before starting & most importantly, Observe & Analyze the problem. Just one good observation can reduce a lot of work of yours !!

SOLUTION :

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Solution to problem - Smartwork vs Hardwork

All the Best !! and Enjoy Reading the solution !!

Keep Learning !

Problem 3 : Smartwork > Hardwork

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Problem Description :

An arrangement of several ‘charged’ discs is done such that all of them subtend the same solid angle Ω at point A. This arrangement is shown in the figure below. The discs are charged positively and negatively alternately (starting with positive first). Magnitude of surface charge density of charged discs is ‘σo’ .

‘x’ is the distance from point A representing the position (used to actually point out the location of discs). It is given as :

                                                                                          x = nxo          ….(I)

     where,   n belongs to natural numbers

                    xo is a constant

Also, similarly the surface charge density (σ) can be represented as a function (for clarity) as :

                                                                                 σ = (-1)n + 1 σo         .…(II)

Question Parts : 

(a)   when x = xo , the radius of the disc is 2Ro . Find the function of radius of the disc (R) as a function of x using constants xo , Ro  

 

(b) The radius of the last disc (for greatest n) in this arrangement is 42 Ro . Find the Electric field at point A due to the whole system. 

(c) All these discs are merged together giving rise to a single disc of ‘some’ pattern. A negatively charged black coloured ink is made to be put over this merged disc. Draw down the final presentation of the disc. (Optional)

Hint : ‘n’ represents the disc number in the arrangement shown in the figure

Enjoy Solving !!

Solution has been uploaded  – SOLUTION

Solution 2 : Bhelpuri Problem !?

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Here we have the solution to our Bhelpuri Problem !!

TIP :

Go through the solution thoroughly. Get an idea of the setup of the problem. If needed, before starting to read the solution once again go and have a look at the problem statement. The problem has a lot of concepts mixed together and that’s how it gets it’s name ‘Bhelpuri‘. So try to go step by step. The solution will guide you to build a procedure in order to finally solve the problem

I have attached the flowchart below in order to get the process. But the flowchart is just to be used as a reference while going through the solution.

Flowchart :

Solution to the Problem :

The solution has been attached in the form of PDF below. Go through it carefully.  Atleast I will say that I personally got to learn a lot while framing this problem & I am sure you will also feel the same after reading the solution !!

Topics Covered : 
  • Plotting graphs (Maths Portion)
  • Collision topic in Center of Mass
  • Projectile Motion
  • Somewhat Electrostatics
  • Basics of electric circuit

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Final Solution-to-Bhelpuri-Problem-2

Keep Learning !

Solution 1 : Chess OR Physics ?

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

Problem Statement (Click Here)

This solution is designed for everyone, whether you are beginner, intermediate or Advanced. The solution has been written in a very lucid language. The reason is simple ! Let’s just keep everything easy. The solution is very detailed and if read it slowly and thoroughly, I am sure that you will get a very deep insight into the concept of center of mass (COM). Enjoy Reading & 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 PDF file after the 3 flowcharts)

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 Rotational motion chapter)
Download the PDF File (Click Here) Solution for Chess OR Physics _

Physics & Electronics Originals (Until Now) :

Keep Learning !

Problem 2 : Bhelpuri Problem !?

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Problem Statement :

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

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

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

Fig. Circuit Schematic

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

Question : 

If this is the case, then what should be the magnitude of the electric field required in order 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 ?

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  • Author – Saurabh Salvi

Watch the video at 1.25x speed if it’s a bit slow for you

Problem 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 ?

*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 !!

Solution has been uploaded. You can check it out with the link below !!

SOLUTION 

Enjoy Solving !!