Measuring Instruments And Least Count
While measuring a metal rod with a vernier caliper of least count 0.01 cm, the main scale reads 3.2 cm and the sixth vernier division coincides with a main-scale line; what is the rod's length?
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About This Question
- Subject
- physics
- Chapter
- physics and measurement
- Topic
- measuring instruments and least count
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
3.26 cm
Reading a vernier caliper combines the main-scale value with a fractional correction read from the coinciding vernier division. The total length equals the main-scale reading plus the product of the coinciding vernier division number and the least count. Here the main-scale reading is 3.2 cm, the coinciding vernier division is the sixth, and the least count is 0.01 cm, so the vernier contribution is 6 × 0.01 = 0.06 cm. Adding these gives a length of 3.2 + 0.06 = 3.26 cm. The choice 3.20 cm ignores the vernier reading altogether and reports only the main scale. The choice 3.60 cm incorrectly treats the vernier contribution as 0.4 cm, misplacing the decimal of the least count. The choice 3.06 cm wrongly reduces the main-scale reading while keeping the vernier part. This is precisely the reading method described in NCERT laboratory work for the vernier caliper. As a plausibility check, the vernier addition can never exceed one full main-scale division of 0.1 cm, and 0.06 cm comfortably satisfies that limit, confirming 3.26 cm.
This medium difficulty physics question is from the chapter physics and measurement, covering the topic of measuring instruments and least count. It appeared in the 2025 exam.
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