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Units and Measurement

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Question : 6 of 33
Marks: +1, -0
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:  
The most precise device is that whose least count is minimum.
Now :
(a) Least count of vernier callipers = 1 MSD – 1 VSD
=1MSD−1920MSD=1 \text{MSD} - \frac{19}{20} \text{MSD}
=120MSD=120mm= \frac{1}{20} \text{MSD} = \frac{1}{20} \text{mm}
=1200cm=0.005cm= \frac{1}{200} \text{cm} = 0.005 \text{cm}
(b) Least count of screw gauge
=pitchno. of divisions on circular scale= \frac{\text{pitch}}{\text{no. of divisions on circular scale}}
=1100mm= \frac{1}{100} \text{mm}
=11000cm= \frac{1}{1000} \text{cm}
=0.001cm= 0.001 \text{cm}
(c) Wavelength of light, λ≃10−5cm=0.00001cm\lambda \simeq 10-5 \text{cm} = 0.00001 \text{cm}
∴ Least count of optical instrument =0.00001cm= 0.00001 \text{cm}
Thus, clearly the optical instrument is the most precise.
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