A student measured the diamenter of a small steel ball using screw gauge of least count 0.001 cm . The scale reading is 5 mm and zero of circular scale division coincides with 25 division above the reference level. If screw gauge has a zero error of `-0.004` cm, the correct diameter of the ball is

Options

A. `0.53 cm`
B. `0.525 cm`
C. `0.521 cm`
D. `0.529 cm`

Explanation

To find the correct diameter of the steel ball measured by the screw gauge, we can follow these steps:

### Step 1: Understand the Measurements
- The main scale reading (MSR) is given as 5 mm.
- The circular scale reading (CSR) is given as the 25th division.
- The least count (LC) of the screw gauge is 0.001 cm.
- The zero error is -0.004 cm.

### Step 2: Convert Measurements to Consistent Units
- Convert the main scale reading from mm to cm:
\[ \text{MSR} = 5 \text{ mm} = 0.5 \text{ cm} \]

### Step 3: Calculate the Circular Scale Reading
- The circular scale reading (CSR) in cm can be calculated as:
\[ \text{CSR} = \text{Number of divisions} \times \text{Least Count} = 25 \times 0.001 \text{ cm} = 0.025 \text{ cm} \]

### Step 4: Calculate the Total Reading Before Adjusting for Zero Error
- The total reading (TR) before adjusting for the zero error is:
\[ \text{TR} = \text{MSR} + \text{CSR} = 0.5 \text{ cm} + 0.025 \text{ cm} = 0.525 \text{ cm} \]

### Step 5: Adjust for Zero Error
- Since the zero error is -0.004 cm, we need to add this value to the total reading:
\[ \text{Correct Diameter} = \text{TR} - \text{Zero Error} = 0.525 \text{ cm} - (-0.004 \text{ cm}) = 0.525 \text{ cm} + 0.004 \text{ cm} = 0.529 \text{ cm} \]

### Final Answer
The correct diameter of the steel ball is:
\[ \text{Correct Diameter} = 0.529 \text{ cm} \]