Question

The pitch of a screw gauge is $0.5\text{mm}$ and there are $100$divisions on its circular scale. The instrument reads $+2$ divisions when nothing is put in between its jaws. In measuring the diameter of a wire, there are $8$ divisions on the main scale and $83$ divisions coincide with the reference line, then the diameter of the wire is?

• A. 4.05mm
• B. 4.405mm
• C. 3.05mm
• D. 1.25mm

Answer 1

The correct option is B

4.405mm

Step 1: Given data

$\text{pitch}=0.5\text{mm}$

$\text{circular scale division}=83$

Step 2: To find

Diameter of the wire

Step 3: Calculate diameter of the wire

$$\begin{gathered} D=\frac{\text{pitch}}{\text{Total CSD}}\times \text{circular scale division}+8\times \text{pitch}-\frac{\text{pitch}}{\text{Total division}}\times 2 \\ =\frac{0.5}{100}\times 83+8\times 0.5-\frac{0.5}{100}\times 2 \\ =4.405\text{mm} \end{gathered}$$

Hence, option (B) is correct.