Step 1: Understanding the Concept:
Measuring with Vernier calipers involves determining the main scale reading (MSR), the Vernier scale reading (VSR), and accounting for any zero error. Zero error occurs when the zeros of the main and Vernier scales do not align when the jaws are closed.
Step 2: Key Formula or Approach:
1. Zero Error ($e$) = $+ (n \times LC)$ if the Vernier zero is to the right (positive error).
2. Total Reading = $(MSR + VSR \times LC) - (\text{Zero Error})$.
Step 3: Detailed Explanation:
1. Calculate Zero Error: Since the Vernier zero is to the right, it is a positive zero error.
\[ e = +(6 \times 0.1 \, \text{mm}) = +0.6 \, \text{mm} = +0.06 \, \text{cm} \]
2. Identify Observed Reading:
- Main Scale Reading ($MSR$) = 3.2 cm (since the zero lies between 3.2 and 3.3).
- Vernier Scale Reading ($VSR$) = 4th division.
- Observed Value = $3.2 + (4 \times 0.01 \, \text{cm}) = 3.24 \, \text{cm}$.
3. Calculate Corrected Diameter:
\[ \text{Diameter} = \text{Observed Value} - \text{Zero Error} \]
\[ \text{Diameter} = 3.24 \, \text{cm} - 0.06 \, \text{cm} = 3.18 \, \text{cm} \]
Step 4: Final Answer
The diameter of the bob is 3.18 cm.