Question

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 the main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is

• A. 0.052 cm
• B. 0.52 cm
• C. 0.026 cm
• D. 0.26 cm

Answer 1

The Correct Option is A

To determine the diameter of the wire using the screw gauge readings provided, we need to understand the reading process of a screw gauge.

Given:

• Main scale reading (MSR) = 0 mm
• Circular scale reading (CSR) = 52 divisions
• 1 mm on the main scale corresponds to 100 divisions on the circular scale.

Step-by-step Calculation:

1. The least count (LC) of the screw gauge is calculated by dividing 1 mm by the number of divisions on the circular scale: \[\text{Least Count (LC)} = \frac{1 \text{ mm}}{100} = 0.01 \text{ mm}\]
2. The total reading (TR) of the screw gauge is given by the sum of the main scale reading (MSR) and the product of the circular scale reading (CSR) and the least count (LC): \[\text{Total Reading (TR)} = \text{MSR} + (\text{CSR} \times \text{LC})\]
3. Substituting the given values: \[\text{TR} = 0 \text{ mm} + (52 \times 0.01 \text{ mm})\] \[\text{TR} = 0.52 \text{ mm}\]
4. Convert the reading from millimeters to centimeters: \[0.52 \text{ mm} = 0.052 \text{ cm}\]

Thus, the diameter of the wire is 0.052 cm.

Conclusion:

The correct answer is 0.052 cm, which matches the given option 0.052 cm.