Question

Which of the following instruments has minimum least count ?

• A. A vernier callipers with $20$ divisions on the vernier scale coinciding with $19$ main scale divisions
• B. A screw gauge of pitch $1 \,mm$ and $100$ divisions on the circular scale
• C. A spherometer of pitch $0.1\, mm$ and $100$ divisions on the circular scale
• D. An optical instrument that can measure length to within a wavelength of light

Answer 1

Answer: (D)

(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.