Question

The pitch of a screw gauge is 1 mm and there are 100 division on its circular scale. When nothing is put in between its jaws, the zero of the circular scale lies 4 divisions below the reference line. When a steel wire is placed between the jaws, two main scale divisions are clearly visible and 67 divisions on the circular scale are observed. The diameter of the wire is

• A. 2.71 mm
• B. 2.67 mm
• C. 2.63 mm
• D. 2.65 mm

Answer 1

The correct option is C 2.63 mm

p =1mm, N =100
Least count, $C=\frac{P}{N}=\frac{1mm}{100}=0.01mm$
The instrument has a positive zero error $e=+NC=+4\times 0.01=+0.04mm$
Main scale reading is $2\times$ (1 mm) = 2 mm
Circular scale reading is 67 (0.01) = 0.67 mm
$\therefore$ Observed reading is $R_0=2+0.67=2.67mm$
So true reading $=R_0-e=2.63mm$