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Vernier Calipers

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While measuring a rod, the main scale of a vernier calipers of least count 0.1 mm reads 4.5 cm and the seventh vernier division coincides with a main scale mark exactly.

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About This Question

Subject
physics
Chapter
experimental skills
Topic
vernier calipers
Difficulty
Medium
Year
2025
Tags
vernier readingcoinciding divisionleast count productmain scale readingfinal measurement

Solution

Correct Answer:

4.57 cm

According to NCERT Class 11, Chapter 2, the total reading of a vernier calipers is obtained by adding the vernier scale contribution to the main scale reading, where the vernier contribution equals the coinciding division number multiplied by the least count. The main scale reading is the largest main scale mark just before the zero of the vernier, here 4.5 cm. The vernier contribution is the coinciding division times the least count: mm cm. Adding gives the final measurement cm. The value 4.70 cm is wrong because it misplaces the decimal, treating 0.7 mm as 0.2 cm too large or adding 0.20 cm. The value 4.507 cm is wrong because it uses a least count of 0.01 mm, appropriate to a screw gauge rather than this vernier. The value 5.20 cm is wrong because it adds 0.7 cm rather than 0.07 cm, an order-of-magnitude slip. Before recording, the instrument should be checked for zero error by closing the jaws fully; any offset would be added to or subtracted from this reading, though none is mentioned here so the reading stands as measured. Keeping consistent units throughout, converting the millimetre-based vernier contribution to centimetres to match the main scale, is the single most common place students make mistakes in this calculation. A plausibility check confirms the correction 0.07 cm is smaller than one main scale division of 0.1 cm, which is exactly the range a vernier fine reading should occupy, so 4.57 cm is internally consistent.

This medium difficulty physics question is from the chapter experimental skills, covering the topic of vernier calipers. It appeared in the 2025 exam.

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