(a)You are given a thread 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 measurements only?

Answer:

(a) Wrap the thread around a pencil several times to produce a coil with the turns close together. Using a metre scale, determine the length of this coil. The diameter of the thread is provided by the following relation if L is the length of the coil and n is the number of turns of the coil.

Diameter = L/n

(b) Least count of the screw gauge = Pitch/number of divisions on the circular scale.

As a result, increasing the number of divisions on the circular scale should reduce the screw gauge’s least count. As a result, the screw gauge’s accuracy will improve. However, this is simply a hypothesis. When the number of turns is raised, there will be many more challenges.

(c) In 100 observations, the likelihood of committing random errors is lowered to a greater extent than in 5 observations.