JEE Main 2022 · 29 July · morning · Single correct · +4 / −1
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?
- (a) 0.001 cm
- (b) 0.002 mm
- (c) 0.002 cm
- (d) 0.005 cm
Answer and solution
Answer (c) 0.002 cm
Solution
Physics sir · 3 steps
Least count is one main scale division minus one vernier division. The total of 50 divisions is a decoy.
- One main division. There are 20 divisions in 1 cm, so 1 MSD = 1/20 cm = 0.05 cm.
- One vernier division. 25 VSD cover 24 MSD, so 1 VSD = 24/25 MSD. Only this coincidence ratio matters. The total of 50 vernier divisions does not enter the least count.
LC = 1 MSD - 1 VSD = 1/25 MSD = 0.05/25 cm
- So. LC = 0.002 cm, which is option (c).
The idea to keep. Find the coincidence first: if n VSD equal (n-1) MSD, the least count is (1 MSD)/n. Use n from that coincidence, not the total number of vernier divisions.
Answer from the NTA final answer key. Solution by PrepWiser.