In an angle-measuring instrument, 29 main-scale divisions coincide with 30 vernier-scale divisions. One main-scale division is 0.5°. If the least count is 1°/(10n), find n.
Physics · Mixed Chapter
JEE Mains

Question

In an angle-measuring instrument, 29 main-scale divisions coincide with 30 vernier-scale divisions. One main-scale division is 0.5°. If the least count is 1°/(10n), find n.

G1 Physics · Accepted Answer

Step 1 — Relation between main and vernier divisions: 30 VSD = 29 MSD ⇒ 1 VSD = (29/30) MSD. Step 2 — Least count: LC = 1 MSD−1 VSD = (1/30) MSD. Step 3 — Insert one MSD = 0.5°: LC = 0.5°/30 = 1°/60. Step 4 — Compare with 1°/(10n): 10n = 60 ⇒ n = 6. Answer: 6.