Two full turns of circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of division on the circular scale is 50. Further, it is found that are the screw gauge has a zero error of -0.03 mm. while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale division, in line with the main scale, as 35. The diameter of the wire is $\frac{338}{20 n} mm$ find the value of ‘n’

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answer is 5.

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Detailed Solution

Least count of the screw gauge,
$\frac{0 .5 mm}{50} = 0 .01 mm$
Main scale reading=3 mm
Vernier scale reading =35
$∴ observed reading = 3 + 0.35 = 3.35 mm$
Zero error = -0.03mm
$∴ Actual diameter of the wire = 3 .35 - (- 0 .03) = 3 .38 mm$

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