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Question

# Pitch of a screw gauge is 1 mm and there are 50 divisions on circular scale. When screw gauge is completely closed 28th division of circular scale coincides with reference line. When a sheet is placed in it, the linear scale reads 2 divisions and circular scale reads 16 divisions. Zero of linear scale is visible when screw gauge is completely closed. Thickness of the sheet is:

A
32 mm
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B
2.88 mm
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C
1.76 mm
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D
2.12 mm
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Solution

## The correct option is C 1.76 mmGiven: Pitch, p=1 mm Divisions on circular scale, N=50 At zero error occurs, 28th circular scale division coincides with the reference line. Measured Main scale reading is at 2 main scale divisions and 16 circular scale divisions. Least count is the ratio of pitch and the number of divisions on circular scale. Hence, least count is: L=pN Zero error, Z=28L Measured main scale reading, MSR=2p Measured circular scale reading, CSR=16L Corrected reading is: C=MSR+CSR−Z C=2p+16L−28L C=2p−12L C=2p−12×pN C=2p(1−6N) C=2×1 mm×(1−650) C=1.76 mm

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