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

(i) The diameter of a thread is so small that it cannot be measured using a metre scale. To measure the diameter of the thread, we wind a number of turns of the thread on the metre scale so that the turns are closely touching one another. Count the number of turns (n) and measure the length (l) of the coiled thread using the metre scale.

Diameter of thread = Length of coiled thread (l) / Number of turns (n)
(ii) Yes, the accuracy of the gauge can be increased by increasing the number of divisions on the circular scale as the least count of the screw gauge is given by

Least count = Pitch / Number of divisions on circular scale
From the formula, it is clear that by increasing the number of divisions on circular scale. Least count can he decreased, hence the accuracy will increase.
It is correct theoretically but practically it may not be possible because it is difficult to take the reading precisely as the resolution of human eye is not so high.

(iii) The mean diameter of a thin brass rod measured by a vernier callipers from a set of 100 measurements is more reliable than the diameter obtained from a set of 5 measurements because the probability of making a positive random error is equal to the probability of making a negative random error. Therefore, in a large number of measurements these errors cancel each other and we get more reliable value.