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Two measuring instruments are described below. Based on the given specifications, choose the correct statement about their least counts. (i) A vernier caliper has main scale divisions of 0.05 cm each, and the vernier scale is divided such that 50 vernier divisions span 2.45 cm. (ii) A screw gauge has a pitch of 0.5 mm, and its circular (thimble) scale has divisions such that one division corresponds to 0.01 mm.

1. Both instruments have the same least count
2. The least count of the screw gauge is smaller than that of the vernier caliper
3. Both instruments have the same least count, but the screw gauge is more precise
4. The two instruments have different least counts, and the screw gauge is more precise

Correct answer: Both instruments have the same least count

Solution

Vernier LC = 1 MSD - 1 VSD = 0.05 cm - (2.45/50) cm = 0.05 - 0.049 = 0.001 cm. Screw gauge LC = 0.01 mm = 0.001 cm. Both have identical least counts of 0.001 cm. Since their least counts are equal, option A is correct.

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