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(a) You are given a thread and a metre scale. How will you estiate the diameter of the thread ?(b) A screw gauge has pitch of 1.0 mm and 200 division on thecircular scale. Do you think it is possiblel to increase the accuracy of the gauge arbitrarily by increasing the number of division on the circular scale ? (c ) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate then a set 5 measurements only? |
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Answer» Solution :(a) The diameter of a thred is so small that it cannot be measurd using a metre scale. We wind a number of turns of the thread on the meter scale so that the turns are CLOSELY toching one another. Measure the length (I) of the winding on the scale which contains n number of turns :. Diameter of thred = `(I)/(n)` (b) As least count=` ("pithc")/("number of divisions on circular scale")` :. theoretically SPEAKING least count decreases on increasing the number of divisions on the ciruclar scale. HENCE, accuracy would increase. Practically it may not be possible to take the reading precisely due to LOW resoulation of human eye. (c ) A large number of observaions (say, 100) will given more reliable result then smaller number of observations (say 5). This is bacuse of probability of making a positive random error of certain magnitude is equal to that of making a negative randow error of the same magnitude. Therefore, when number of observations is large, randow error are likely to cancel and the result may be morel reliable. |
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