Two full turns of the circular scale of a screw gauge cover a distance of `1mm` on its main scale. The total number of divisions on the circular scale is `50`. Further, it is found that the screw gauge has a zero error of `- 0.03mm`. While main scale reading of `3mm` and the number of circular scale divisions in line with the main scale as `35`. the dimeter of the wire is

Options

A. `3.32mm`
B. `3.73 mm`
C. `3.67 mm`
D. `3.38 mm`

Answer

D

Explanation

According to given details when circular scale of screw gauge covers a distance of 1mm, upon two circular turns.
The distance covered by the screw gauge in axial direction upon its one revolution is called the pitch of screw gauge.
Here, pitch `=(1)/(2)mm =0.5mm`
Least count (LC) `=("Pitch")/("Number of divisions on circular scale")`
`=(0.5mm)/(50)=0.01mm`
Main scale reading MSR= 3mm
Circular scale reading CSR= 35
Zero error is = -0.3mm
Reading noted by student
MSR= 3mm, CSR= 35
The diameter of wire is
`D= MSR+CSRxxLC+ZE`
`=3mm+35xx0.01mm+(-0.03)mm`
`3.38mm`