Question

Two full turns of the circular scale of a screw gauge cover a distance of $1 \, mm$ 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 $-0.03 \, mm$ . While measuring the diameter of a thin wire, a student notes the main scale reading of $3 \, mm$ and the number of circular scale divisions, in line with the main scale, as $35$ . The diameter of the wire is

• A. $\text{3.38} \, mm$
• B. $\text{3.32}mm$
• C. $\text{3.73}mm$
• D. $\text{3.67}mm$

Answer 1

Answer: (A)

Least count of the screw gauge,
$=\frac{\text{0.5 mm}}{\text{50}}=\text{0.01} \, mm$
Main scale reading $=3 \, mm$
Vernier scale reading $=35$
$\therefore $ Observed reading $=3+\text{0.35}=\text{3.35 mm}$
Zero error $=\text{-0.03} \, mm$
$\therefore $ Actual diameter of the wire $=\text{3.35}-\left(- \text{0.03}\right)=\text{3.38} \, mm$