Question

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?​

Answer 1

Explanation:

(a) Least count of this vernier callipers = 1SD - 1 VD = 1 SD - 19/20 SD = 1/20 SD

= 1.20 mm = 1/200 cm = 0.005 cm

(b) Least count of screw gauge = Pitch/Number of divisions = 1/1000 = 0.001 cm.

(c) Wavelength of light, λ ≈ 10-5 cm = 0.00001 cm

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

Answer 2

(a)  Least count of vernier callipers

= 1 MSD - 1 VSD

= 1 MSD - 19/20 MSD = 1/20 MSD

= 1/20 mm = 1/200 cm = 0.005 cm

(b) Least count of screw gauge pitch / no of divisions on circular scale

= 1 / 100 mm = 1 / 1000 cm = 0.001 cm

(c) Wavelength  of light  λ = $10^{-5}$ cm

= 0.00001 cm

Thus, clearly the optical instrument is the most precise.