The length is measured using a vernier system whose main scale is 30 cm long with 600 divisions. If 19 divisions of the main scale coincide with 20 divisions of the vernier scale, then its least count is

Question

The length is measured using a vernier system whose main scale is 30 cm long with 600 divisions. If 19 divisions of the main scale coincide with 20 divisions of the vernier scale, then its least count is (A) 0.25 cm (B) 0.025 cm (C) 0.25 mm (D) 0.025 mm

Tardigrade Admin · Accepted Answer

∵ Least count =M S D-V S D ∵ MSD =(((30/100))/600)=5 × 10-4 m and VSD =(19/20) × MSD =(19/20) × 5 × 10-4=4.75 × 10-4 ∴ Least count =(5-4.75) × 10-4=0.025 mm

Q. The length is measured using a vernier system whose main scale is $30 c m$ long with $600$ divisions. If $19$ divisions of the main scale coincide with $20$ divisions of the vernier scale, then its least count is

0.25 cm

0.025 cm

0.25 mm

0.025 mm

0.0025

$∵$ Least count $= MS D - V S D$
$∵ MS D = \frac{( \frac{30}{100} )}{600} = 5 \times 1 0^{- 4} m$
and $V S D = \frac{19}{20} \times MS D$
$= \frac{19}{20} \times 5 \times 1 0^{- 4} = 4.75 \times 1 0^{- 4}$
$∴$ Least count $= (5 - 4.75) \times 1 0^{- 4} = 0.025 mm$

Q. The length is measured using a vernier system whose main scale is 30cm long with 600 divisions. If 19 divisions of the main scale coincide with 20 divisions of the vernier scale, then its least count is