How will you estimate the diameter of the thread

Answer the following:

(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?

Solution:

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

thread?

Take a uniform cylindrical smooth rod and Wrap the thread in such a way that the turns of thread are tight and touch each immediate neighboring turns. Now measure the length of the thread using a metre scale.

The diameter of the thread = distance between first and last turn / number of turns

 (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?

Least count of a screw gauge = length of pitch/number of division

Theoretically we can increase the accuracy of screw gauge by decreasing length of pitch or increasing number of divisions. But practically we cannot decrease length of pitch or increase number of divisions from a contain limit. So accuracy cannot increase from a limit.

(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?

 Accuracy of a measurement can be increase with increase of number of observations hence 100 measurements is more reliable than a set of 5 measurements.