Monday 10 June 2013

সময় কি এবং সময়ের অস্তিত্বের কারণ কি ?

এক সময় পদার্থ বিদ্যায় সময় কে আমাদের মস্তিস্কর উপজ বলে চিহ্নিত করা হত । তখনকার দিনে  বলা হতো সময় ঠিক করে বলতে গেলে এমন একটা জিনিস যা একসঙ্গে  সবকিছুকে ঘটতে দেয়না । এমন কি  আলবার্ট আইনস্টাইন বলেছিলেন  যে এই জগতে অতীত  এবং ভবিষ্যত এক মরিচিকা  ছাড়া আর কিছুই নয়, মানুষের ভ্রম মাত্র । কিন্তু  সত্যি করে বলতে গেলে  সময় কি আর কেন আমরা সময় কে উপলব্ধি করতে পারি তার কোনো সঠিক ব্যাখ্যা  নেই ।

Time waits for no man: A small portion of one of the largest seen star-birth regions in the galaxy, the Carina Nebula, taken by Hubble telescope, 2010

তবে সম্প্রতি পদার্থ বিজ্ঞানীরা এটা বের করার চেষ্টা করছেন যে সত্যি সত্যি  বলতে গেলে কেন এই বিশাল বিশ্ব ব্রহ্মান্ড সময়ের উপর নির্ভরশীল । কেন আমরা সময়ের গতিকে পরিচালিত করতে পারিনা, কেন এই বিশ্ব ব্রহ্মান্ড সুচারু রূপে  চলতে গেলে সময়ের উপর নির্ভরশীল হয়ে পরে ? কেও কেও আবার বলছেন সময় বলে কিছু নেই যা অবিরত চলতে থাকে , বরঞ্চ এটা  বলা যেতে পারে কি সময় অনেকটা বালুকা দানার মতন । আবার কিছু মানুষ আছেন যারা বলে চলেছেন যে সময়ের একটি নয় বরঞ্চ দুটি দিক আছে ।



Once upon a time, physicists liked to dismiss those who dwelled too much on the passing of the seconds, days and years. They wrote off the apparent flow of time as a trick of the mind. They joked that time is what keeps everything from happening at once. Albert Einstein, who believed the distinction between the past and future is an illusion, declared that time is “what you measure with a clock”.
In recent years, however, physicists have been working around the clock to find out what makes the cosmos tick. Some suggest that there is not a continuous flow of time, but rather spacetime moments trickling like grains of sand through an hourglass. Others say that there should be two dimensions of time, not one (so called “hypertime” jettisons the pesky headache of time travel, which is allowed by current theory); or that time, not being fundamental, was born in the Big Bang and could grind to a halt in a few billion years; or, according to the British philosopher Julian Barbour, time does not exist because we dwell within a heap of moments, each an instant of frozen time.
Quite a few feel that an overhaul of what we mean by “time” could lead to the next great leap in physics. Among them is Lee Smolin, of the Perimeter Institute for Theoretical Physics in Canada. Smolin argues that science is blighted by what he says are unreal and inessential conceptions of time. He insists that “time is real” and that its reformulation could be central to finding the long-sought after “theory of everything”.
In Time Reborn, he offers an entertaining, head-spinning and, yes, timely blend of philosophy, science, and speculation to put the Now back into physics.
The problem with time dates back centuries. The physical laws outlined by greatest figure of the Scientific Revolution, Isaac Newton, are indifferent to the direction of time and suggest the future is determined by the past. Thus, as the French mathematician Pierre-Simon Laplacefamously pointed out, we may regard the present state of the universe as the effect of its past and the cause of its future. And if our future’s already written, then the things that are most valuable about being human are illusions, along with time itself.
Ever since Newton, physicists have been developing ever more exact laws describing the behaviours of the world. These laws don’t change. They are more real than time. They are timeless truths. “If laws are outside of time, then they’re inexplicable,” says Smolin. “If we want to understand law then law must evolve, law must change, law must be subject to time. Law then emerges from time and is subject to time rather than the reverse.”
He cites heavyweights such as the Briton Paul Dirac and the American philosopher Charles Sanders Peirce who have also suggested that the laws of physics evolve. In an earlier book, Smolin outlined one somewhat hairy scheme to explain how this may occur: universes reproduce inside black holes and, as in Darwin’s natural selection, those with parameters for spawning new black holes have offspring; those that do not fizzle out. The laws become fine-tuned, changes accumulating each time a baby cosmos is born. This daisy chain of descendant universes unfolds in time, and Smolin believes that this is real time.
Guided by an insight from Newton's great rival, Gottfried Leibnitz, Smolin’s picture of the cosmos violates Einstein's relativity because it requires an absolute time, preferred global time. To make time real, he also puts forward a weird idea, “the principle of precedence”, that repeated measurements of a certain phenomenon yield the same outcomes not because it obeys a law of nature but simply because the phenomenon is a habit. This would allow new measurements to yield new outcomes, not predictable from knowledge of the past.Thus the future becomes open once more.
A few years ago, Smolin triggered much heated debate with The Trouble with Physics in which he argued that attempts to explain the fundamentals of the universe by the dominant paradigm of so-called string theory, which comes in many flavours, remain untested “because they make no clean predictions or because the predictions they do make are not testable”. The problem is that the ideas in Time Reborn feel just as wildly speculative, if not more so.
Still, his maverick meditations serve as a reminder that it’s hard to find a consensus on the future of physics at an exciting time when it feels like everything could be altered in an eye-blink by the findings from extraordinary experiments under way to probe the puzzles of dark matter, dark energy, antimatter and more. That is the physicists’ ultimate arrow of time, pointing from today’s understanding towards the next great mystery.


Wednesday 21 November 2012

MOCK EXAM PAPER FOR PRACTICE; EME-101; ENGINEERING MECHANICS


Printed Pages:4                                    Paper Code: EME-101                                                     


 
B.  Tech –1st Year (SEM.I)
Pre University Examination, May2012 – 13
Engg.Mechanics
Time:   3hrs                                                                 Total Marks:  100                                        
Note:   (1)        Attempt all questions.
(2)        Be precise in your answer.
Section-A
Tick the appropriate answer:
1. Three forces P, 2P and 3P are exerted along the directions of three sides of equilateral triangle. Their Resultant is 
  a) √3P               b) 3√3P               c) 3P                d) none of the above
2. If two forces P and Q act at an angle Ө, the resultant of these two forces would make an angle α with P such that  
 a) tan α = Q Sin Ө  /  P-Q Sin Ө         b) tan α = P Sin Ө  / P+ Q Sin Ө       
 c) tan α = Q Sin Ө / P+ Q Cos Ө        d) tan α= P Sin Ө / Q - P Cos Ө  
3. The center of gravity of a semicircle  of radius r made of metal is 
 a) on the base                           b) on the perimeter             
 c) 3r/8 above the base              d) 4r/3π above the base.
4. The parallel axis theorem for moment of inertia is
 a) Izz = Ixx + Iyy                           b) IGx= Ixx + AY2             
 c) IGx= Ixx - AY2                         d)   IGx= Ixx + AX2                 
Fill in the blanks:
5. A body is on the point of sliding down an inclined plane under its own weight. If the inclination of the plane to the horizontal is 30° degree the angle of friction will be----------------------.
6. The velocity of a particle falling from a height h just  before touching ground is ---------------
7. A beam is having more than two supports is called---------------------- beam and such beams are statically   -----------------.
8. A car moving with uniform acceleration covers 450m in a 5 seconds and covers 700m in the next 5 seconds interval. The acceleration of the car is……………. .m /s2.
9. Varignon’s theorem is related to……………
10. A truss is said to be rigid in nature when there is no --------------- on application of any external --------------------.             (2x 10=20)

Section-B
Attempt any two parts from each question.           (3x10 = 30)

 Q.1. (a) Define parallelogram law of forces and lami’s theorem.

(b) Find the resultant of the force system given in figure-2, Also find its position:
 (c) A uniform ladder weighting 200 N and length 6m is placed against a vertical wall in a position where its inclination to the vertical is 30 degree. A man weighting 600N climbs the ladder. At what position will he induce slipping? Take coefficient of friction μ = 0.2 at both the contact surfaces of ladder.

Q.2(a) How are the trusses classified? What are the assumptions taken while analyzing a plane truss?

 (b) Draw the reactions for the beam AB loaded through the attached strut.
 (c) Find the reaction in the cantilever beam shown in figure:

Q.3. (a) Define Parallel axis theorem and Perpendicular axis theorem.

(b) Find the Moment of Inertia of the I section shown in figure-5 about x-x and y-y axes.
(c) Derive an expression for mass moment of inertia of a right circular cone of base  radius R, height H and mass M about its axis.   

Section-C
 (5x10=50)   
Q.1. (a) Define impulse. State and explain the D'Alemberts principle.
(b) The equation of motion of a particle moving in a straight line is given by  the equation s =16t +4t2-3t3 where s is the total distance covered from the starting  point in meter at the end of t seconds. Find
(i) Displacement, velocity and acceleration 2 seconds after the start
(ii) the displacement and acceleration when velocity is zero
(iii) the maximum velocity of the particle.

(c)
Define the following terms:    i) inertial force (ii) angle of repose (iii) coplanar non concurrent force system (iv) angular momentum 

 
Q.2(a) A car moving with an constant acceleration from rest in the first 50 sec, then in the next 40 second it moves with a constant velocity, in the next 20 second it comes to rest. Find the maximum and average velocity and the acceleration of the car:

(b)