Which of the following is the most precise devise for measuring length ? (a) a Vernier callipers with 20 divisions on the sliding scals, coindiing with 19 main scale divions (b) a screw gauge of pitch 1mm and 100 divisions on the circular scale (c ) an optical instrument that can measure length to within a wave length of light.

Explanation

The most precise device is that whose least count is minimum. Now
(a) Least count of theis vernier callipers ` = 1 SD -1VD = 1SD -(19)/(20)SD = (1)/(20)SD`
`=(1)/(20)mm = (1)/(200) = 0.005cm`
(b) Least count of screw gauge ` = ("pitch")/("no. of divisonsn on circular scale") = (1)/(100)mm = (1)/(1000) cm = 0.001cm`.
(c ) Wavelength of light,`lambda ~~ 10^(-5)cm. =0.00001cm`.
Obviousoly, the most precise measurement is with optical instrument.