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  4. In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation the reading on the main scale is 5 mm and the 20 text th division of the circular scale coincides with reference line. Calculate the true reading.

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Q. In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are $50$ divisions on the circular scale, and the main scale moves by $0.5 \,mm$ on a complete rotation. For a particular observation the reading on the main scale is $5\, mm$ and the $20^{\text {th }}$ division of the circular scale coincides with reference line. Calculate the true reading.

JEE MainJEE Main 2021Physical World, Units and Measurements

Solution:

Least count (L.C) $=\frac{0.5}{50}$
True reading $=5+\frac{0.5}{50} \times 20-\frac{0.5}{50} \times 5$
$=5+\frac{0.5}{50}(15)=5.15\, mm$