Sphere Diameter Measurement Using Screw Gauge with Zero Error

To find the correct diameter of the sphere, we follow these steps:

1. Calculation of Least Count ($\text{LC}$)

The least count of a screw gauge is defined as the ratio of pitch to the total number of divisions on the circular scale: $\text{LC} = \frac{\text{Pitch}}{\text{Total circular scale divisions}} = \frac{0.1 \text{ mm}}{100} = 0.001 \text{ mm}$

2. Determination of Zero Error ($\text{ZE}$)

When the two studs are in contact, the $5^{\text{th}}$ division of the circular scale coincides with the main scale reference line. This indicates a positive zero error: $\text{Zero Error (ZE)} = +5 \times \text{LC} = +5 \times 0.001 \text{ mm} = +0.005 \text{ mm}$

3. Calculation of Observed Reading

When measuring the diameter of the sphere:

• $\text{Main Scale Reading (MSR)} = 5 \text{ mm}$
• $\text{Circular Scale Division (CSD)} = 50$
• $\text{Circular Scale Reading (CSR)} = \text{CSD} \times \text{LC} = 50 \times 0.001 \text{ mm} = 0.050 \text{ mm}$

$\text{Observed Reading} = \text{MSR} + \text{CSR} = 5 \text{ mm} + 0.050 \text{ mm} = 5.050 \text{ mm}$

4. Calculation of True Diameter

The true measurement is obtained by subtracting the zero error from the observed reading: $\text{True Diameter} = \text{Observed Reading} - \text{Zero Error}$ $\text{True Diameter} = 5.050 \text{ mm} - (+0.005 \text{ mm}) = 5.045 \text{ mm}$

Hence, the correct option is A.