Question

Pitch of a screw gauge is 1 mm and there are 50 divisions on circular scale. When screw gauge is completely closed ${28}^{th}$ 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
• B. 2.88 mm
• C. 1.76 mm
• D. 2.12 mm

Answer 1

The correct option is C 1.76 mm

Given:

• Pitch, $p=1mm$
• 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:
$L=\frac{p}{N}$

Zero error, $Z=28L$

Measured main scale reading, $MSR=2p$
Measured circular scale reading, $CSR=16L$

Corrected reading is:
$C=MSR+CSR-Z$
$C=2p+16L-28L$
$C=2p-12L$
$C=2p-12\times \frac{p}{N}$
$C=2p(1-\frac{6}{N})$
$C=2\times 1mm\times (1-\frac{6}{50})$
$C=1.76mm$