Question

The pitch of an error free screw gauge is 1 mm and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads 1 mm and 63^rd division on the circular scale coincides with the reference line. The diameter of the wire is:

• A. 1.63 cm
• B. 0.163 cm
• C. 0.163 m
• D. 1.63 m

Answer 1

The Correct Option is B

1. Least Count (LC) of screw gauge

$$ \text{LC} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}} $$

$$ \text{LC} = \frac{1 \, \text{mm}}{100} = 0.01 \, \text{mm} $$

2. Observed readings 

$$ \text{Main Scale Reading (MSR)} = 1 \, \text{mm} $$ $$ \text{Circular Scale Reading (CSR)} = 63 \, \text{divisions} $$

3. Total reading formula

$$ \text{Final Reading} = \text{MSR} + (\text{CSR} \times \text{LC}) $$

$$ = 1 \, \text{mm} + 63 \times 0.01 \, \text{mm} $$

$$ = 1 \, \text{mm} + 0.63 \, \text{mm} $$

$$ = 1.63 \, \text{mm} $$