Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.
Reason R : Least Count `= ("Pitch")/("Total divisionson circular scale")`
In the light of the above statements, choose the most appropriate answer from the options given below :

Options

A. A is not correct but R is correct.
B. Both A and R are correct and R is the correct explanation of A.
C. A is correct but R is not correct.
D. Both A and R are correct and R is NOT the correct explanation of A.

Answer

To solve the problem, we need to analyze both the Assertion (A) and the Reason (R) given in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that if in five complete rotations of the circular scale, the distance travelled on the main scale of the screw gauge is 5 mm, and there are 50 total divisions on the circular scale, then the least count is 0.001 cm.

2. **Calculating the Pitch**:
- The pitch of the screw gauge is defined as the distance moved by the main scale for one complete rotation of the circular scale.
- Given that in 5 complete rotations, the distance travelled is 5 mm, we can find the pitch:
\[ \text{Pitch} = \frac{\text{Distance travelled}}{\text{Number of rotations}} = \frac{5 \text{ mm}}{5} = 1 \text{ mm} \]

3. **Finding the Least Count**:
- The formula for the least count (LC) of a screw gauge is given by:
\[ \text{Least Count} = \frac{\text{Pitch}}{\text{Total divisions on circular scale}} \]
- Substituting the values we have:
\[ \text{Least Count} = \frac{1 \text{ mm}}{50} = 0.02 \text{ mm} \]

4. **Converting to cm**:
- To convert the least count from mm to cm:
\[ 0.02 \text{ mm} = 0.02 \times \frac{1 \text{ cm}}{10 \text{ mm}} = 0.002 \text{ cm} \]

5. **Conclusion on Assertion**:
- The assertion states that the least count is 0.001 cm, but we calculated it to be 0.002 cm. Therefore, the assertion is incorrect.

6. **Understanding the Reason (R)**:
- The reason states that the least count is calculated using the formula provided, which is indeed correct.

7. **Conclusion on Reason**:
- The reason is correct as it accurately describes how to calculate the least count.

### Final Conclusion:
- The assertion (A) is incorrect, while the reason (R) is correct.

### Answer:
- Therefore, the correct answer is that the assertion is incorrect and the reason is correct.

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