Question:

Which of the following instruments has minimum least count ?

Updated On: Jul 7, 2022
  • A vernier callipers with $20$ divisions on the vernier scale coinciding with $19$ main scale divisions
  • A screw gauge of pitch $1 \,mm$ and $100$ divisions on the circular scale
  • A spherometer of pitch $0.1\, mm$ and $100$ divisions on the circular scale
  • An optical instrument that can measure length to within a wavelength of light
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The Correct Option is D

Solution and Explanation

(a) Least count of vernier callipers $=1\,MSD-1\,VSD=1\,MSD-\frac{19}{20}\,MSD$ $=\frac{1}{20}\,MSD=\frac{1}{20}\,mm=\frac{1}{200}\,cm=0.005\,cm$ $\left(\because 1\,MSD=1\,mm\right)$ (b) Least count of screw gauge $=\frac{\text{Pitch}}{\text{No.of divisions on circular scale}}$ $=\frac{1}{100}\,mm=\frac{1}{1000}\,cm$ $=0.001\,cm$ (c) Least count of spherometer $=\frac{\text{Pitch}}{\text{No.of divisions on circular scale}}$ $=\frac{0.1\,mm}{100}=\frac{1}{1000}\,mm$ $=0.0001\,cm$ (d) Wavelength of light, $\lambda = 10^{-5}\, cm = 0.00001 \,cm$ Clearly the optical instrument is the most precise.
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Concepts Used:

Units and Measurement

Unit:

A unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by the society and in terms of which other quantities of similar nature may be measured.

Measurement:

The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.

Read More: Fundamental and Derived Units of Measurement

System of Units:

  1. CGS system
  2. FPS system
  3. MKS system
  4. SI units

Types of Units:

Fundamental Units -

The units defined for the fundamental quantities are called fundamental units.

Derived Units -

The units of all other physical quantities which are derived from the fundamental units are called the derived units.