(solved)Question 2.6 of NCERT Class XI Physics Chapter 2

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?

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Parveen,

Question 2.6
NCERT Class XI Physics

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 ?

Soln. Method I: by Physical Concept

Precision is the smallest distance (i.e., least count) that a device can measure.

Both Vernier Callipers and Screw Gauge are used directly with a naked eye so their least count is going to be much much higher than the least count of optical instruments that can indirectly measure to a thickness of the order of the wavelength of light.

Hence optical instruments are the most precise - Ans!

Soln. Method II: by Calculations

The given VC will have $\displaystyle 19 \text{ mm}$ divided into $\displaystyle 20$ divisions.

$ \begin{aligned} \text{LC of the VC }&= 1 - \frac{19 \text{ mm }}{20} \\ \\ &= \frac{1}{20} \text{ mm} = 5 \times 10^{-5} \text{ m} \end{aligned} $

The LC of screw gauge is $\displaystyle \frac{1 \text{ mm}}{100} = 10^{-5} \text{ m}$

LC of optical instruments $\displaystyle 5000 \text{ Å} = 5 \times 10^{-7}\text{ m}$

By comparison, the LC of optical instruments is the smallest. Hence they are the most precise - Ans!

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