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An angle-measuring device is such that 29 main-scale divisions line up exactly with 30 vernier-scale divisions. If one main-scale division equals 0.5°, what is the least count of the instrument?
- 30 seconds
- 1°
- 0.5°
- 1 minute
Correct answer: 1 minute
Solution
The least count is determined by the difference between one main-scale division and one vernier-scale division. Since 29 main-scale divisions equal 30 vernier divisions, the value of one vernier division is 0.5°/29, which is approximately 0.01724°. The least count, being the smallest measurable angle, is then calculated as 1 main-scale division (0.5°) minus 1 vernier division (0.01724°), resulting in a least count of 1 minute.
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