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, we need to understand the relationship between the main scale and the circular scale.

1. The Main Scale Reading (MSR) is given as \(0 \, \text{mm}\).
2. The Circular Scale Reading (CSR) is given as \(52\) divisions. 
3. It's also provided that \(1 \, \text{mm}\) on the main scale corresponds to \(100\) divisions on the circular scale. Hence, each division on the circular scale corresponds to: \(\frac{1}{100} \, \text{mm} = 0.01 \, \text{mm}\)
4. The total reading on the screw gauge is calculated as follows: \(\text{Total Reading} = \text{MSR} + (\text{CSR} \times \text{Least Count})\)
5. Substituting the values, we have: \(\text{Total Reading} = 0 \, \text{mm} + (52 \times 0.01 \, \text{mm})\)
6. This simplifies to: \(\text{Total Reading} = 0.52 \, \text{mm}\)
7. Convert the measurement from millimeters to centimeters, since the options are in centimeters: \(0.52 \, \text{mm} = 0.052 \, \text{cm}\)
8. Therefore, the diameter of the wire is: 0.052 cm.
9. Comparing with the given options, the correct answer is 0.052 cm. This matches with the provided correct answer choice.

This clear step-by-step computation explains why the diameter of the wire measures 0.052 cm.