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Units And Measurement

Question
CBSEENPH11019874

Which of the following is the most precise device for measuring length : 

(a) a vernier callipers with 20 divisions on the sliding scale

b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale

(c) an optical instrument that can measure length to within a wavelength of light.


Solution

A device with minimum count is the most suitable to measure length.
a) 
straight L. straight C space of space vernier space calliper space equals space 1 space straight S. straight D space minus space 1 space straight V. straight D

space space space space space space space space space space space space space space space space space equals space 1 space minus space 9 over 10 space equals space 1 over 10 space equals space 0.01 space cm  
b) 
straight L. straight C space of space screw space gauge space equals space fraction numerator Pitch over denominator Number space of space divisions end fraction space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 over 1000 space equals space 0.001 space cm space

straight c right parenthesis

straight L. straight C space of space an space optical space device space equals space Wavelength space of space light space tilde 10 to the power of negative 5 end exponent space cm space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 0.00001 space cm 

Hence, it can be inferred that an optical instrument is the most suitable device to measure length.