A slender shaft supported on two bearings at its ends carries a disc with an eccentricity e from the axis of rotation. The critical speed of the shaft is Nc. If the disc is replaced by a second one of same mass but mounted with an eccentricily 2 e, t ?->(Show Answer!)

1. A slender shaft supported on two bearings at its ends carries a disc with an eccentricity e from the axis of rotation. The critical speed of the shaft is Nc. If the disc is replaced by a second one of same mass but mounted with an eccentricily 2 e, then the critical speed of the shaft in the second case is

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MCQ->A slender shaft supported on two bearings at its ends carries a disc with an eccentricity e from the axis of rotation. The critical speed of the shaft is Nc. If the disc is replaced by a second one of same mass but mounted with an eccentricily 2 e, then the critical speed of the shaft in the second case is....

MCQ-> Our propensity to look out for regularities, and to impose laws upon nature, leads to the psychological phenomenon of dogmatic thinking or, more generally, dogmatic behaviour: we expect regularities everywhere and attempt to find them even where there are none; events which do not yield to these attempts we are inclined to treat as a kind of `background noise’; and we stick to our expectations even when they are inadequate and we ought to accept defeat. This dogmatism is to some extent necessary. It is demanded by a situation which can only be dealt with by forcing our conjectures upon the world. Moreover, this dogmatism allows us to approach a good theory in stages, by way of approximations: if we accept defeat too easily, we may prevent ourselves from finding that we were very nearly right.It is clear that this dogmatic attitude; which makes us stick to our first impressions, is indicative of a strong belief; while a critical attitude, which is ready to modify its tenets, which admits doubt and demands tests, is indicative of a weaker belief. Now according to Hume’s theory, and to the popular theory, the strength of a belief should be a product of repetition; thus it should always grow with experience, and always be greater in less primitive persons. But dogmatic thinking, an uncontrolled wish to impose regularities, a manifest pleasure in rites and in repetition as such, is characteristic of primitives and children; and increasing experience and maturity sometimes create an attitude of caution and criticism rather than of dogmatism.My logical criticism of Hume’s psychological theory, and the considerations connected with it, may seem a little removed from the field of the philosophy of science. But the distinction between dogmatic and critical thinking, or the dogmatic and the critical attitude, brings us right back to our central problem. For the dogmatic attitude is clearly related to the tendency to verify our laws and schemata by seeking to apply them and to confirm them, even to the point of neglecting refutations, whereas the critical attitude is one of readiness to change them - to test them; to refute them; to falsify them, if possible. This suggests that we may identify the critical attitude with the scientific attitude, and the dogmatic attitude with the one which we have described as pseudo-scientific. It further suggests that genetically speaking the pseudo-scientific attitude is more primitive than, and prior to, the scientific attitude: that it is a pre-scientific attitude. And this primitivity or priority also has its logical aspect. For the critical attitude is not so much opposed to the dogmatic attitude as super-imposed upon it: criticism must be directed against existing and influential beliefs in need of critical revision – in other words, dogmatic beliefs. A critical attitude needs for its raw material, as it were, theories or beliefs which are held more or less dogmatically.Thus, science must begin with myths, and with the criticism of myths; neither with the collection of observations, nor with the invention of experiments, but with the critical discussion of myths, and of magical techniques and practices. The scientific tradition is distinguished from the pre-scientific tradition in having two layers. Like the latter, it passes on its theories; but it also passes on a critical attitude towards them. The theories are passed on, not as dogmas, but rather with the challenge to discuss them and improve upon them.The critical attitude, the tradition of free discussion of theories with the aim of discovering their weak spots so that they may be improved upon, is the attitude of reasonableness, of rationality. From the point of view here developed, all laws, all theories, remain essentially tentative, or conjectural, or hypothetical, even when we feel unable to doubt them any longer. Before a theory has been refuted we can never know in what way it may have to be modified.In the context of science, according to the passage, the interaction of dogmatic beliefs and critical attitude can be best described as:
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MCQ-> Read the passage carefully and answer the questions given at the end of each passage:We now come to the second part of our journey under the sea. The first ended with the moving scene in the coral cemetery which left a deep impression on my mind. I could no longer content myself with the theory which satisfied Conseil. That worthy fellow persisted in seeing in the Commander of the Nautilus one of those unknown servants who returns mankind contempt for indifference. For him, he was a misunderstood genius who, tired of earth’s deceptions, had taken refuge in this inaccessible medium, where he might follow his instincts freely. To my mind, this explains but one side of Captain Nemo’s character. Indeed, the mystery of that last night during which we had been chained in prison, the sleep, and the precaution so violently taken by the Captain of snatching from my eyes the glass I had raised to sweep the horizon, the mortal wound of the man, due to an unaccountable shock of the Nautilus, all put me on a new track. No; Captain Nemo was not satisfied with shunning man. His formidable apparatus not only suited his instinct of freedom, but perhaps also the design of some terrible retaliation. That day, at noon, the second officer came to take the altitude of the sun. I mounted the platform, and watched the operation. As he was taking observations with the sextant, one of the sailors of the Nautilus (the strong man who had accompanied us on our first submarine excursion to the Island of Crespo) came to clean the glasses of the lantern. I examined the fittings of the apparatus, the strength of which was increased a hundredfold by lenticular rings, placed similar to those in a lighthouse, and which projected their brilliance in a horizontal plane. The electric lamp was combined in such a way as to give its most powerful light. Indeed, it was produced in vacuo, which insured both its steadiness and its intensity. This vacuum economized the graphite points between which the luminous arc was developed - an important point of economy for Captain Nemo, who could not easily have replaced them; and under these conditions their waste was imperceptible. When the Nautilus was ready to continue its submarine journey, I went down to the saloon. The panel was closed, and the course marked direct west. We were furrowing the waters of the Indian Ocean, a vast liquid plain, with a surface of 1,200,000,000 of acres, and whose waters are so clear and transparent that any one leaning over them would turn giddy. The Nautilus usually floated between fifty and a hundred fathoms deep. We went on so for some days. To anyone but myself, who had a great love for the sea, the hours would have seemed long and monotonous; but the daily walks on the platform, when I steeped myself in the reviving air of the ocean, the sight of the rich waters through the windows of the saloon, the books in the library, the compiling of my memoirs, took up all my time, and left me not a moment of ennui or weariness. From the 21 st to the 23 rd of January the Nautilus went at the rate of two hundred and fifty leagues in twenty- four hours, being five hundred and forty miles, or twenty-two miles an hour. If we recognized so many different varieties of fish, it was because, attracted by the electric light, they tried to follow us; the greater part, however, were soon distanced by our speed, though some kept their place in the waters of the Nautilus for a time. The morning of the 24 th , we observed Keeling Island, a coral formation, planted with magnificent cocos, and which had been visited by Mr. Darwin and Captain Fitzroy. The Nautilus skirted the shores of this desert island for a little distance. Soon Keeling Island disappeared from the horizon, and our course was directed to the north- west in the direction of the Indian Peninsula. From Keeling Island our course was slower and more variable, often taking us into great depths. Several times they made use of the inclined planes, which certain internal levers placed obliquely to the waterline. I observed that in the upper regions the water was always colder in the high levels than at the surface of the sea. On the 25th of January the ocean was entirely deserted; the Nautilus passed the day on the surface, beating the waves with its powerful screw and making them rebound to a great height. Three parts of this day I spent on the platform. I watched the sea. Nothing on the horizon till about four o’clock then there was a steamer running west on our counter. Her masts were visible for an instant, but she could not see the Nautilus, being too low in the water. I fancied this steamboat belonged to the P.O. Company, which runs from Ceylon to Sydney, touching at King George’s Point and Melbourne. At five o’clock in the evening, before that fleeting twilight which binds night to day in tropical zones, Conseil and I were astonished by a curious spectacle. It was a shoal of Argonauts travelling along on the surface of the ocean. We could count several hundreds. These graceful molluscs moved backwards by means of their locomotive tube, through which they propelled the water already drawn in. Of their eight tentacles, six were elongated, and stretched out floating on the water, whilst the other two, rolled up flat, were spread to the wing like a light sail. I saw their spiral-shaped and fluted shells, which Cuvier justly compares to an elegant skiff. For nearly an hour the Nautilus floated in the midst of this shoal of molluscs. The next day, 26 th of January, we cut the equator at the eighty-second meridian and entered the northern hemisphere. During the day a formidable troop of sharks accompanied us. They were “cestracio philippi” sharks, with brown backs and whitish bellies, armed with eleven rows of teeth, their throat being marked with a large black spot surrounded with white like an eye. There were also some Isabella sharks, with rounded snouts marked with dark spots. These powerful creatures often hurled themselves at the windows of the saloon with such violence as to make us feel very insecure. But the Nautilus, accelerating her speed, easily left the most rapid of them behind.About seven o’clock in the evening, the Nautilus, half- immersed, was sailing in a sea of milk. At first sight the ocean seemed lactified. Was it the effect of the lunar rays? No; for the moon, scarcely two days old, was still lying hidden under the horizon in the rays of the sun. The whole sky, though lit by the sidereal rays, seemed black by contrast with the whiteness of the waters. Conseil could not believe his eyes, and questioned me as to the cause of this strange phenomenon. Happily I was able to answer him. “It is called a milk sea,” I explained. “A large extent of white waves is often to be seen on the coasts of Amboyna, and in these parts of the sea.” “But, sir,” said Conseil, “can you tell me what causes such an effect? For I suppose the water is not really turned into milk.” “No, my boy; and the whiteness which surprises you is caused only by the presence of myriads of luminous little worm, gelatinous and without colour, of the thickness of a hair, and whose length is not more than seven-thousandths of an inch. These insects adhere to one another sometimes for several leagues.” “Several leagues!” exclaimed Conseil. “Yes, my boy; and you need not try to compute the number of these infusoria. You will not be able, for, if I am not mistaken, ships have floated on these milk seas for more than forty miles.” Towards midnight the sea suddenly resumed its usual colour; but behind us, even to the limits of the horizon, the sky reflected the whitened waves, and for a long time seemed impregnated with the vague glimmerings of an aurora borealisFind the TRUE Sentence:
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MCQ-> Read the following passage carefully and answer the questions given at the end. When Ratan Tata moved the Supreme Court, claiming his right to privacy had been violated, he called Harish Salve. The choice was not surprising. The former solicitor general had been topping the legal charts ever since he scripted a surprising win for Mukesh Ambani against his brother Anil. That dispute set the gold standard for legal fees. On Mukesh’s side were Salve, Rohinton Nariman, and Abhishek Manu Singhvi. The younger brother had an equally formidable line-up led by Ram Jethmalani and Mukul Rohatgi.The dispute dated back three-and-a-half years to when Anil filed case against his brother for reneging on an agreement to supply 28 million cubic metres of gas per day from its Krishna-Godavari basin fields at a rate of $ 2.34 for 17 years. The average legal fee was Rs. 25 lakh for a full day's appearance, not to mention the overnight stays at Mumbai's five-star suites, business class travel, and on occasion, use of the private jet. Little wonder though that Salve agreed to take on Tata’s case pro bono. He could afford philanthropy with one of India’s wealthiest tycoons.The lawyers’ fees alone, at a conservative estimate, must have cost the Ambanis at least Rs. 15 crore each. Both the brothers had booked their legal teams in the same hotel, first the Oberoi and, after the 26/ ll Mumbai attacks, the Trident. lt’s not the essentials as much as the frills that raise eyebrows. The veteran Jethmalani is surprisingly the most modest in his fees since he does not charge rates according to the strength of the client's purse. But as the crises have multiplied, lawyers‘fees have exploded.The 50 court hearings in the Haldia Petrochemicals vs. the West Bengal Government cost the former a total of Rs. 25 crore in lawyer fees and the 20 hearings in the Bombay Mill Case, which dragged on for three years, cost the mill owners almost Rs. 10 crore. Large corporate firms, which engage star counsels on behalf of the client, also need to know their quirks. For instance, Salve will only accept the first brief. He will never be the second counsel in a case. Some lawyers prefer to be paid partly in cash but the best are content with cheques. Some expect the client not to blink while picking up a dinner tab of Rs. 1.75 lakh at a Chennai five star. A lawyer is known to carry his home linen and curtains with him while travelling on work. A firm may even have to pick up a hot Vertu phone of the moment or a Jaeger-LeCoutre watch of the hour to keep a lawyer in good humour.Some are even paid to not appear at all for the other side - Aryama Sundaram was retained by Anil Ambani in the gas feud but he did not fight the case. Or take Raytheon when it was fighting the Jindals. Raytheon had paid seven top lawyers a retainer fee of Rs. 2.5 lakh each just to ensure that the Jindals would not be able to make a proper case on a taxation issue. They miscalculated when a star lawyer fought the case at the last minute. “I don’t take negative retainers”, shrugs Rohatgi, former additional solicitor general. “A Lawyer’s job is to appear for any client that comes to him. lt’s not for the lawyers to judge if a client is good or bad but the court”. Indeed. He is, after all, the lawyer who argued so famously in court that B. Ramalinga Raju did not ‘fudge any account in the Satyam Case. All he did was “window dressing”.Some high profile cases have continued for years, providing a steady source of income, from the Scindia succession battle which dates to 1989, to the JetLite Sahara battle now in taxation arbitration to the BCCI which is currently in litigation with Lalit Modi, Rajasthan Royals and Kings XI Punjab.Think of the large law firms as the big Hollywood studios and the senior counsel as the superstar. There are a few familiar faces to be found in most of the big ticket cases, whether it is the Ambani gas case, Vodafone taxation or Bombay Mills case. Explains Salve, “There is a reason why we have more than one senior advocate on a case. When you're arguing, he’s reading the court. He picks up a point or a vibe that you may have missed.” Says Rajan Karanjawala, whose firm has prepared the briefs for cases ranging from the Tata's recent right to privacy case to Karisma Kapoor’s divorce, “The four jewels in the crown today are Salve, Rohatgi, Rohinton Nariman and Singhvi. They have replaced the old guard of Fali Nariman, Soli Sorabjee, Ashok Desai and K.K. Venugopal.” He adds, “The one person who defies the generational gap is Jethmalani who was India's leading criminal lawyer in the 1960s and is so today.”The demand for superstar lawyers has far outstripped the supply. So a one-man show by, say, Rohatgi can run up billings of Rs. 40 crore, the same as a mid-sized corporate law firm like Titus and Co that employs 28 juniors. The big law filik such as AZB or Amarchand & Mangaldas or Luthra & Luthra have to do all the groundwork for the counsel, from humouring the clerk to ensure the A-lister turns up on the hearing day to sourcing appropriate foreign judgments in emerging areas such as environmental and patent laws. “We are partners in this. There are so few lawyers and so many matters,” points out Diljeet Titus.As the trust between individuals has broken down, governments have questioned corporates and corporates are questioning each other, and an array of new issues has come up. The courts have become stronger. “The lawyer,” says Sundaram, with the flourish that has seen him pick up many Dhurandhares and Senakas at pricey art auctions, “has emerged as the modern day purohit.” Each purohit is head priest of a particular style. Says Karanjawala, “Harish is the closest example in today's bar to Fali Nariman; Rohinton has the best law library in his brain; Mukul is easily India's busiest lawyer while Manu Singhvi is the greatest multi-tasker.” Salve has managed a fine balancing act where he has represented Mulayam Singh Yadav and Mayawati, Parkash Singh Badal and Amarinder Singh, Lalit Modi and Subhash Chandra and even the Ambani brothers, of course in different cases. Jethmalani is the man to call for anyone in trouble. In judicial circles he is known as the first resort for the last resort. Even Jethmalani’s junior Satish Maneshinde, who came to Mumbai in I993 as a penniless law graduate from Karnataka, shot to fame (and wealth) after he got bail for Sanjay Dutt in 1996. Now he owns a plush office in Worli and has become a one-stop shop for celebrities in trouble.Which of the following is not true about Ram Jethmalani?
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MCQ-> Analyse the following passage and provide appropriate answers for the questions that follow: Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected. The principal of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific “truth.” But what is the source of knowledge? Where do the laws that are to be tested come from? Experiment, itself, helps to produce these laws, in the sense that it gives us hints. But also needed is imagination to create from these laws, in the sense that it gives us hints. But also needed is imagination to create from these hints the great generalizations – to guess at the wonderful, simple, but very strange patterns beneath them all, and then to experiment to check again whether we have made the right guess. This imagining process is so difficult that there is a division of labour in physics: there are theoretical physicists who imagine, deduce, and guess at new laws, but do not experiment; and then there are experimental physicists who experiment, imagine, deduce, and guess. We said that the laws of nature are approximate: that we first find the “wrong” ones, and then we find the “right” ones. Now, how can an experiment be “wrong”? First, in a trivial way: the apparatus can be faulty and you did not notice. But these things are easily fixed and checked back and forth. So without snatching at such minor things, how can the results of an experiment be wrong? Only by being inaccurate. For example, the mass of an object never seems to change; a spinning top has the same weight as a still one. So a “law” was invented: mass is constant, independent of speed. That “law” is now found to be incorrect. Mass is found is to increase with velocity, but appreciable increase requires velocities near that of light. A true law is: if an object moves with a speed of less than one hundred miles a second the mass is constant to within one part in a million. In some such approximate form this is a correct law. So in practice one might think that the new law makes no significant difference. Well, yes and no. For ordinary speeds we can certainly forget it and use the simple constant mass law as a good approximation. But for high speeds we are wrong, and the higher the speed, the wrong we are. Finally, and most interesting, philosophically we are completely wrong with the approximate law. Our entire picture of the world has to be altered even though the mass changes only by a little bit. This is a very peculiar thing about the philosophy, or the ideas, behind the laws. Even a very small effect sometimes requires profound changes to our ideas.Which of the following options is DEFINITLY NOT an approximation to the complete truth?
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