The length of the string of a simple pendulum is measured with a meter scale to be `63.5 cm`, the radius of the bob plus the hook is measured with the help of vernier caliper to be `1.55 cm`. Select the incorrect statement.

Options

A. Least count of meter scale is `0.1 cm`
B. Least count of vernier caliper is `0.01 cm`
C. Effective length of pendulum is `65.0 cm`
D. Effective length of pendulum is `65.2 cm`

Explanation

To solve the problem, we need to analyze the given measurements and determine the incorrect statement based on the least counts and significant figures.

### Step-by-Step Solution:

1. **Identify the Measurements:**
- Length of the string of the pendulum (measured with a meter scale): \( L = 63.5 \, \text{cm} \)
- Radius of the bob plus hook (measured with a vernier caliper): \( r = 1.55 \, \text{cm} \)

2. **Determine the Least Count of the Meter Scale:**
- The meter scale has 10 divisions in 1 cm.
- Therefore, the least count (LC) of the meter scale is:
\[ LC_{\text{meter scale}} = \frac{1 \, \text{cm}}{10} = 0.1 \, \text{cm} \]

3. **Determine the Least Count of the Vernier Caliper:**
- The vernier caliper has 10 divisions in 1 mm (or 0.1 cm).
- Therefore, the least count (LC) of the vernier caliper is:
\[ LC_{\text{vernier caliper}} = \frac{0.1 \, \text{cm}}{10} = 0.01 \, \text{cm} \]

4. **Calculate the Effective Length of the Pendulum:**
- The effective length \( L_{\text{effective}} \) of the pendulum is the sum of the length of the string and the radius of the bob plus hook:
\[ L_{\text{effective}} = L + r = 63.5 \, \text{cm} + 1.55 \, \text{cm} = 65.05 \, \text{cm} \]

5. **Apply Significant Figures:**
- The measurement \( 63.5 \, \text{cm} \) has 3 significant figures, and \( 1.55 \, \text{cm} \) also has 3 significant figures.
- Therefore, the result should be reported with 3 significant figures:
\[ L_{\text{effective}} = 65.0 \, \text{cm} \]
- The last digit is rounded down because the following digit (5) is not significant in this context.

6. **Identify the Incorrect Statement:**
- Based on the calculations:
- The least count of the meter scale is correctly calculated as \( 0.1 \, \text{cm} \).
- The least count of the vernier caliper is correctly calculated as \( 0.01 \, \text{cm} \).
- The effective length of the pendulum is correctly reported as \( 65.0 \, \text{cm} \).
- Therefore, the statement that contradicts any of these findings is the incorrect statement.

### Conclusion:
The incorrect statement is the one that does not align with the calculated values of least counts or the effective length of the pendulum.

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