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A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?

Asked in JEE Main 29th July 1st Shift 2022 · Least count of a travelling microscope

Answer: (3) 0.002 cm

Step-by-step solution

Step 1: one main scale division.

20 divisions per cm, so 1 MSD=0.05 cm.

Step 2: use the matching condition, not the total division count.

25 VSD=24 MSD gives 1 VSD=0.96 MSD.

Step 3: LC=1 MSD-1 VSD=0.04×0.05=0.002 cm.

The '50 divisions' in the stem is there to mislead: what fixes the least count is the 25:24 matching, not how many divisions are engraved.

Why the other options are wrong

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