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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 mm
Given:
  • 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+CSRZ
C=2p+16L28L
C=2p12L
C=2p12×pN
C=2p(16N)
C=2×1 mm×(1650)
C=1.76 mm

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