Original Problems

We have another Physics problem here !

The problem is a kind of blend of physics and electronics which made this problem to fall in this section. The problem is multi-concept based. As a hint, the problem mixes up :

• Kinematics
• A bit of rotational motion
• Electronics (Understanding of Resistor)

As a reference, you can use the attached article so that you are all covered to complete this problem : Click Here

The Problem Statement has been uploaded below in the form of PDF. 

DOWNLOAD

Problem 7

For the Best Experience, View on Desktop/Laptop !

Problem Description : 

Three containers are kept on a horizontal surface. The dimensions of all the containers is given in Fig.1 . The base of each container is kept on a pressure sensor (PS). Each container is placed below a tap. All containers are symmetrical about the central axis. The whole setup is shown in Fig. 2

• Pressure Sensor/ Pressure Transducer:

        For this problem, we have chosen this sensor to measure the pressure                at the base

 

• Working: 

         More the pressure, more the value sent as output

         Note : In reality, this is known as a force sensor

The pressure sensor is further, a part of the electric circuit shown. The circuit involves :

• Microcontroller – Arduino
• Pressure Sensor
• LED
• LDR
• Multimeter as Ammeter

Hint : LDR stands for ‘Light’ Dependent Resistor

Note : Each container has a separate circuit (Fig.3) for itself attached

Arduino IDE code:

Hint : Understand the problem statement, the setup of the problem, the circuit and the code thoroughly. Note that, you just need to get the gist of what the code is trying to do!

• Based on your understanding,

                Answer the Question Parts shown below

Question Parts :

Part- (a)

The taps above respective containers are turned on and water is allowed to flow into the containers. The experimenter keeps a track of the height of the water column ‘h’ which gets accumulated in the containers w.r.t time and plots the graphs for the same as an observation. (Taps are not identical)*

Graphs are as follows :

• Is there any time instant where the readings of the current values are same on atleast 2 ammeters? And if you find any, then find the volume of water filled in the 3 containers at that time instant.

Part-(b)

Part-(c)

• Draw the simplified schematic circuit diagram and a flowchart which simplifies Fig.3

            (Optional)

Conclusion :

Understand & draw the circuit. Try to understand the motive behind the code. Basically, there is a type of procedure/flow to approach this problem. Try to grab that flow.

Solution has been uploaded !! – SOLUTION

All the Best !!

For Best Experience, View on Desktop/Laptop

💎This problem is mainly designed to act as a ‘bridge’ 🌉 between physics students and chess players !!

What I mean by this is that , Physics people need to learn basic chess to solve this, while Chess players need to learn little physics to solve this problem.

Problem Statement :

Two friends decide to play an friendly match. Both of them sit for the match. The following game (given below) has been played on the chessboard by them. The square shaped chessboard has the length of ‘8L’.

Game Notations :

Getting frustrated from the piece loss, player with the Black pieces decides to resign the game and the result of the game is 1-0

Question Parts :

1. With reference to the game played, find out the displacement vector of the white’s g1 knight after the 7^th move from white side has been completed. (Take the origin as the centre of the chessboard)

       2. Does the position of origin matter in the answer of part 1 ?

Assumptions :

Assume the pieces to be point masses and are located at the center of respective squares

(Chess Notations can be observed from figure below)

Solution has been uploaded – SOLUTION

Enjoy Solving !!

For Best Experience, View on Desktop/Laptop

Commentary: Oh! we are witnessing the most exciting final ever. Just look at the score board mate! The crowd is going crazyyy at the Wankhede stadium. For now, We are having some discussion going on between captain and umpires and seems like they have been given a new ball for the last ball of the match.

 Fig. Scoreboard Situation

Commentary: Till the game resumes back, we show you the stats of the players as well as the info of the Wankhede stadium.

Striker :

• Age : 26
• Right handed batsman
• Average : 25.5
• Highest : 67(36)
• Maximum effort chart: (‘v’ in m/s and ‘t’ in s)

                    – Nature of graph : Straight line

                                                                                  Fig. Maximum effort chart for Striker

Non – Striker :

• Age : 27
• Right handed batsman
• Average : 23.2
• Highest : 56(23)*
• Maximum effort chart: (‘v’ in m/s and ‘t’ in s)

– Nature of graph : Parabolic  (It’s a curve involving some parabolas)

(This tells how a player runs between the wickets when he performs at his maximum potential and it’s a pre-recorded data)

                                                                                      Fig. Maximum Effort Chart for Non-Striker

                                                                                    Fig. Circular Shaped Wankhede Stadium

Commentary : Okay, So after a long wait, we are all ready for the play to begin !

What exactly happened?:

**The half portion of the ground (not containing the striker) is introduced with an magnetic field of upwards direction (seems as if it comes out of the ground) having magnitude 0.54 T (tesla)

                                                                                                 Fig. What exactly happened ?

Regarding the New Ball

• Mass : 160 g
• Charge : 164 mC
• Colour : White

Commentary :  Man, I am just out of words…Just picth the ball towards the batsman, I can’t wait anymore.

 So, here we go Guys !….

Match Resumes !!…It’s the last ball now

Commentary : Oh, what a excellent toe crushing yorker just ahead of the stumps, to which batsman replies with a flick towards the leg side. The ball is running towards the boundary along the ground…………….

Commentary : Both the striker and the non striker have started running with their maximum efforts across the pitch, trying their level best !!

                                                                                                Fig. Final Last Ball Situation

In the figure above,

v is the velocity of the ball just after the impact with the bat and theta is the angle which the ball makes with the center pitch line.

Commentary : Hey, watch out! What’s happening in here, I just can’t believe what’s happening, Also, with me, my co-commentator friends, audience as well as the players themselves are just completely astonished.

---

Question Parts :

(a) Why are there only 3 regions in the Maximum Effort Chart of both, striker and non-striker. Are you able to verify, if the                    velocity-time graphs are correct?

(b) In this scenario, can you predict What’s the result of the match!? Also, if you want, you can give some nice commentary as well to describe the situation completely.

(Assume ball to be point mass; there is no friction between ground and the ball )

---

 Some points from my Side :

I feel that this problem is completely comprehensive based. Hint which I can give is that, Try to Extract the necessary information from the comprehension.  These problems are designed to make you enjoy the subject, enjoy the process while solving. No one is there here to reduce your marks, So solve it without any hesitation !!

“I want you to be in that atmosphere as if you are an spectator seeing this match going on in front of your eyes“

Solution has been uploaded !! – SOLUTION 

All the very Best !!

View on Laptop/Desktop for Better Experience

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 ‘σ_o’ .

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

                                                                                          x = nx_o          ….(I)

     where,   n belongs to natural numbers

                    x_o is a constant

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

                                                                                 σ = (-1)^{n + 1} σ_o         .…(II)

Question Parts : 

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

 

(b) The radius of the last disc (for greatest n) in this arrangement is 42 R_o . 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