2.8 Answer the following:

(a) You are given a thread and a meter scale. How will you estimate the diameter of the thread?

(b) A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions 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 than a set of 5 measurements only?

(a) The diameter of a thread is so small that it cannot be measured using a meter scale. We wind a number of turns of the thread on the meter scale so that the turns are closely touching one another. Measure the length (Z) of the windings on the scale which contains n number of turns.
Diameter of thread =1/n
(b) Least count=pitchnumber of divisions on circular scale

So, theoretically, the least count decreases on increasing the number of divisions on the circular scale. Hence, accuracy would increase. Practically, it may not be possible to take the reading precisely due to the low resolution of the human eye.
(c) A large number of observations (say, 100) will give more reliable results than a smaller number of observations (say, 5). This is because the larger the number of readings, the closer is the arithmetic mean to the true value and hence the smaller the random error.