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

Options

A. (a)0.053 cm
B. (b)0.525 cm
C. 0.521 cm
D. (d)0.529 cm

Answer

To find the correct diameter of the small steel ball measured using a screw gauge, we need to follow these steps:

### Step 1: Understand the Measurements
- **Main Scale Reading (MSR)**: The main scale reading is given as 5 mm. We need to convert this to centimeters.

\[ \text{MSR} = 5 \text{ mm} = 0.5 \text{ cm} \]

### Step 2: Calculate the Circular Scale Reading (CSR)
- **Circular Scale Reading (CSR)**: The zero of the circular scale coincides with 25 divisions above the reference level. The least count of the screw gauge is 0.001 cm, which means each division on the circular scale represents 0.001 cm.

\[ \text{CSR} = 25 \text{ divisions} \times 0.001 \text{ cm/division} = 0.025 \text{ cm} \]

### Step 3: Calculate the Total Reading Before Error Correction
- **Total Reading (TR)**: The total reading before correcting for zero error is the sum of the main scale reading and the circular scale reading.

\[ \text{TR} = \text{MSR} + \text{CSR} = 0.5 \text{ cm} + 0.025 \text{ cm} = 0.525 \text{ cm} \]

### Step 4: Account for Zero Error
- **Zero Error**: The screw gauge has a zero error of -0.004 cm. This means the actual measurement is less than the reading by this amount.

\[ \text{Correct Diameter} = \text{TR} - \text{Zero Error} = 0.525 \text{ cm} - (-0.004 \text{ cm}) = 0.525 \text{ cm} + 0.004 \text{ cm} = 0.529 \text{ cm} \]

### Final Answer
The correct diameter of the ball is:

\[ \text{Correct Diameter} = 0.529 \text{ cm} \]