Question

The diagram below shows part of the main scale and Vernier scale of a Vernier caliper, which is used to measure the diameter of a metal ball. Find the least count and the radius of the ball.

A.$0.01cm,2.18cm$
B.$0.02cm,2.18cm$
C.$0.01cm,2.17cm$
D.None of these

Answer 1

Hint:To solve this problem firstly we should learn about the Vernier scale, Least count, Main scale and the concepts behind these terms. We will study all the related information on these topics. And by this information, we can easily approach our answer.

Complete step by step answer:
Vernier scale is a visual aid which is used for accurate measurement, helps in reading between two graduation markings by mechanical interpolation, by using Vernier acuity to reduce human error. It is used for educational purposes, in scientific Research and labs, Machinery, Medical sector, Aerospace sector.
Least count: Least count determining instrument is the smallest and the accurate value in the measured quantity. The least count is associated with the precision of an instrument, an instrument which can detect the smaller changes in a value relative to another instrument.
Main scale: The main scale reading is the primary reading on the main scale immediately to the left of the zero of Vernier scale, While the Vernier scale which exactly coexists with a mark on the main scale.

Least count,
$ = \dfrac{{Value\,of\,one\,main\,scale\,division}}{{Number\,of\,division\,on\,vernier\,scale}}$
$ = \dfrac{{1mm}}{{10}} = \dfrac{{0.1cm}}{{10}}$
$ = 0.01cm$

Reading (diameter)
$MS\,reading + (coinciding\,VS\,reading \times Least\,count$
$ = 4.3cm + \left( {7 \times 0.01} \right)$
$ = 4.3 + 0.07 = 4.37cm$
Diameter$ = 4.37cm$
$\therefore $ Radius$ = \dfrac{{4.37}}{2} = 2.185cm$

So, the correct answer is option A $0.01cm,2.18cm$

Note: Vernier caliper is a measuring device that consists of a main scale with fixed jaw and sliding with an attached Vernier. It is used for educational purposes, in scientific Research and labs, Machinery, Medical sector, Aerospace sector. Vernier calipers require attention while working on it, firstly slide the jaw against the object, Read the main scale with Sliding scale zero. Read the scale and add numbers.