Question 6. A screw gauge gives the following readings when used to measure the diameter of a wire
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:
(1) 0.52 cm
(2) 0.026 cm
(3) 0.26 cm
(4) 0.052 cm
Answer: Option (4)
Explanation:
The least count of a screw gauge is given by:
\text{Least Count} = \frac{\text{Pitch}}{\text{Number of circular scale divisions}}Here,
Pitch = 1 mm
Number of divisions on circular scale = 100
So,
\text{Least Count} = \frac{1}{100} \ \text{mm} = 0.01 \ \text{mm}The diameter of the wire is calculated as:
\text{Reading} = \text{Main scale reading} + (\text{Circular scale reading} \times \text{Least Count})Substituting the values:
\text{Diameter} = 0 + (52 \times 0.01) \ \text{mm} \text{Diameter} = 0.52 \ \text{mm}Converting into cm:
0.52 \ \text{mm} = 0.052 \ \text{cm}Hence, the diameter of the wire is 0.052 \ \text{cm}.
Therefore, the correct option is (4).