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  4. In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm . There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, what is the thickness (in mm) of the wire?

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Q. In a screw gauge, $5$ complete rotations of the screw cause it to move a linear distance of $0.25 \, cm$ . There are $100$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $4$ main scale divisions and $30$ circular scale divisions. Assuming negligible zero error, what is the thickness (in mm) of the wire?

NTA AbhyasNTA Abhyas 2020Physical World, Units and Measurements

Solution:

Least count $=\frac{0 .25}{5 \times 100} \, cm=5\times 10^{- 4} \, cm$
Reading $=4\times 0.05 \, cm+30\times 5\times 10^{- 4} \, cm$
$=\left(0 .2 + 0 .0150\right) \, cm=2.15 \, mm$