Answer the following :
(a) You are given a tread and a metre 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 measurement only ?

Explanation

(a) The diameter of the thread is very small and cannot be measured by a metre scale. Wind the thread in close turns on the metre scale. These turns are closely touching each other. Count the number of turns. Find the average length of the coiled thread on the metre scale. Divide this average length by the number of turns.
Thus, diameter of the thread `=("Average length")/("Number of turns")`.
(b) Yes, the accuracy of the gauge can be increased by increasing the number of divisions on the circular scale because when number of turns increases, the least count of the instrument becomes less.
Because, least count `=("Pitch")/("Number of division on the circular scale")`
(c ) Yes, it is true that when we take a large number of observations say (100) and then take their mean value for the result, the random errors are greatly reduced as compared to the case when we take only five observations and then take their mean. Therefore, the result is more reliable when we take a set of 100 measurements than a set of 5 measurements only.