I was just solving this problem in my XI class and was surprised that almost all books/past IIT published papers I could get my hands on had given an incorrect answer for parts (b) and (c)! Now, this problem is not so difficult that everybody seems to be missing the point…
Curious to know why people were missing the point, I searched the internet for any discussions on this problem and found this webpage: http://www.goiit.com/posts/list/mechanics-block-a-of-mass-m-and-block-b-of-mass-2m-are-placed-1014688.htm;jsessionid=01CD5F97DC80010D43A806A1069FD981.node2#1266894
The person who posted the question posted it as a MCQ with four options, which is not the case as this problem was actually a subjective problem. However, the post’s author was definitely thinking on the right track even though most of the commentators were doing what most books have done - totally missed the point. Guys, wake up: parts (b) and (c) are indeterminate – all you can do is to find some equation/inequality that must be satisfied; but the exact values of friction (and tension) are indeterminate!
There is no reason why the friction on B should become limiting while friction on A does all the self-regulating in order to satisfy the equations! Also note that the string connecting them is in-extensible, so there is no possibility of even a microscopic motion of B while A stays at rest. If the string were a real cotton string (which is slightly extensible), then I may have accepted someone assuming friction on B to be limiting, since B would have shifted down slightly, breaking the friction “interlocking”; thus leaving behind friction on A to manage the equations for system to be static. Although, even in that case, this would have been just one possible outcome as the detailed microscopic dynamics of friction would depend upon things like “exactly when the two blocks are relased from rest”, what is the state of “taut-ness” of the string at that instant, etc.
The “red” coloured massless rigid rod in the diagram rigidly connects the two blocks, while the mass of the blue hanging block has been so chosen that the conditions of the IIT-JEE problem are replicated, minus any ambiguity created if someone does not understand what it means for the string to be ”inextensible”.
Top results from 2012 classroom batch (live classes through fully interactive HD video conferencing in our own, one of a kind, e-hybrid classroom). Total of 20 selections out of a batch of 31 students!
Abhijit Lavania: Tricity Rank 1, All India Rank 27
Akshit Trehan: Tricity Rank 2, All India Rank 85
Lakshay Goel: Tricity Rank 5, All India Rank 276
Our top results in Chandigarh so far… Abhijit Lavania (tri-city topper): JEE Mains 2013 score = 331; cleared Physics Olympiad (in top 5 from India); SAT score = 2330 (Abhijit is sitting on extreme left in the classroom photo above). Akshit Trehan: JEE Mains 2013 score = 315. Lakshay Goel: JEE Mains 2013 score = 310
Anasuya is currently a graduate student at MIT (Massachusetts Institute of Technology, US) and co-founder of a creative media start-up, IndianRaga. She completed her B.Tech in Chemical Engineering from IIT Bombay with a minor in Probability and Statistics.
Learning physics from Sir in those two years leading up to JEE was my formative experience of ‘engineering’. We’d start from calculus and logic and build up to all the complicated Greek renditions that some of our friends told us had to be committed to memory. None of that in Sir’s approach to problem solving. It was the first time I felt empowered to tackle any problem (mostly within our humble JEE syllabus domain ) with only my intellect and some stationery. It was a transformative, rewarding and extremely enjoyable to learn from such a teacher. I still strive to make my figures as pretty and perfect as he used to get them on the board. One of the most striking things I remember is that we always used to look at everything big picture and delve deeper, slowly. It’s something I try to apply everywhere even today, when it’s so easy to get caught up in the details and mess simple things up.
Those two years laid the foundation to where I am today and Sir is one of the most inspiring people I feel I am privileged to have learnt from.
Detailed reflections from Anasuya…
The two years spent in grueling preparation for JEE 2007 were ironically some of the most memorable ones. Days would seem indistinguishable, weeks seemed to be on repeat – Math after Physics after Chemistry – interspersed with occasional namesake school visits. Hours were spent poring over texts, assignments, tests and notes, solving endlessly.
In the beginning, Chauhan Sir’s classes and he himself were intimidating yet awe-inspiring – a batch strength of 150, packed into a sloping classroom, seats based on quiz performances, surprise quizzes that we’d never heard of before. The first register was a huge fat one that all students received. What Sir wrote, we wrote. I scribbled the in-between things I thought I’d need to make sense of the seemingly esoteric ‘physics’ later and strived to make my figures as pretty and immaculate as Sir’s. Hot, scorching summer afternoons spent in an air-conditioned classroom, little by little learning to derive physics from scratch. In many ways, the calculus I learnt there remains more imprinted in my brain than any other text book.
We made our way through Kinematics, slowly and surely, getting things right was the prerogative. The next milestone was Rotational Mechanics – all of us screwed up that test so badly. Electrodynamics, electromagnetics and optics seemed like an eternity and in retrospect, it seems like we whizzed past everything else. By this time also, it was fairly well-established, since the sex-ratio in the classes was almost like IIT (it was 13 guys for each girl in my batch at IIT Bombay) you had to learn to speak up and discuss your doubts with guys. Being shy was not helpful any more and suddenly all the brats became the stars while the girls struggled to keep up, an automatic reversal of the class 10 results situation. Classes involved deriving everything from the basics and never cramming any formulae – a logical progression of steps with everything we ourselves had arrived at, no extraneous input – just logic and calculus and a little help from Newton and Maxwell. Sometimes, Sir would bring his guitar to class and play for us. I, for one, was definitely impressed by the coolness coefficient. Sir was what was epitome of an IITian to me at that time. His philosophies and ‘fundae’ on the most trivial things, yet most profound would be a welcome change to the Greek we’d be scribbling. Post class doubt sessions were fun always, bordering on exhaustion from marathon three hour classes, yet enthused to clarify and discuss. I since haven’t taken such intensive lessons and I think I’ve lost the concentration to be attentive for such a long time-span but back then we were drunk on resolve to succeed. Especially when nearing the final few months, Sir would often play the title track of ‘Lakshya’ for us, motivating and literally brainwashing us.
We would hear anecdotes about single-digit and two-digit rankers, demi-gods in my head back then (I know some of them now and they’re some very stellar individuals) and there was this burning desire to be worthy of being in those ranks, being considered among that class of people. And that was my sole motivation. I secured a three-digit rank that I was decently satisfied with – I could pursue what I thought I wanted to. I was lucky to head to an institute which offered tremendous opportunities.
In many ways, those two years laid the foundation to where I am today and Sir is one of the most inspiring people I feel I am privileged to have learnt from. This article was the least I could do: write out of love and respect for a teacher whose words would echo in my head on so many nights, when I’d lie awake, sleepless and scared of what the future held and whether I’d be able to prove myself worthy of it.
I have always believed that Physics is the backbone of all engineering and technology (of course, Math is an indispensible tool and chem/bio move in a different, and perhaps more important direction); human race will need some very good minds in the next 50 years if we are to evolve as the responsible ‘dominant/caretaker’ species towards the next stage: evolve psychologically, socially, economically as well as technologically. In a way, it is ironical – if all humans are wiped out of earth, no other life form will miss us much; and yet, we humans can be reason for the extinction of a large chunk of our eco-bio-sphere.
Well, ethics cannot be taught or implanted, but I am hopeful that the more the brain functions at a higher level, the more there is empathy and a natural emergence of ethical values.
One small step in that direction, towards encouraging young minds to think deeply and build a strong foundation in science & analytical thinking – “IIT JEE to be subjective from 2014″: http://www.hindustantimes.com/India-news/Mumbai/Subjective-test-proposed-for-IIT-JEE-stage-two/Article1-1037028.aspx
New batch classes will start from 9th April (Tuesday), 2013. We wanted to start earlier (from 5th April), but some parents from out of Chandigarh requested that they needed the first week of April for miscellaneous school admission related tasks, and also to settle their wards in PG accommodation in Chandigarh. XII class days will be Tuesdays, Thursdays and Saturdays. XI class days will be Mondays, Wednesdays and Fridays.
Note: From 25 March to 8 April, XI lectures will be replayed from 10 AM, in this order: Fluids >> Thermodynamics >> Sound. March 26 & 27 will be Holi holidays.
Advanced theory and numerical of the following XI topics will be covered in XII batch during revision time (starting in April 2013), along with Advanced Calculus and its applications in Physics: Rotational Mechanics, Gravitation, SHM & Mechanical Oscillations, Elasticity, Fluid Mechanics, Heat & Thermodynamics, Mechanical Waves & Sound. Revision of these XI topics will be ‘wedged’ in between the XII syllabus.
Check this out! Those aged 13 to 18 can participate in this google science fair/competition.