Question

Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.
Reason R : Least Count = $\frac{\text{Pitch}}{\text{Total divisions on circular scale}}$

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

Hint:

Always be careful with units when calculating the least count. The pitch is usually in millimeters, and the final answer might be required in centimeters or millimeters. A common error is a mistake in unit conversion.

Answer 1

The Correct Option is D

Analysis of Reason (R):
The formula given for the least count of a screw gauge is:
Least Count = Pitch / (Total divisions on circular scale).
This is the correct definition and formula. So, Reason (R) is a correct statement.
Analysis of Assertion (A):
First, we need to calculate the pitch of the screw gauge.
Pitch is the distance moved on the main scale for one complete rotation.
Given: 5 rotations cause a movement of 5 mm.
Pitch = $\frac{5 \text{ mm}}{5 \text{ rotations}} = 1$ mm.
Now, we calculate the least count using the formula from Reason (R).
Total divisions on circular scale = 50.
Least Count (LC) = $\frac{1 \text{ mm}}{50} = 0.02$ mm.
The assertion states that the least count is 0.001 cm. Let's convert our calculated LC to cm.
Since 1 cm = 10 mm, 1 mm = 0.1 cm.
LC = $0.02 \text{ mm} = 0.02 \times 0.1 \text{ cm} = 0.002$ cm.
The calculated least count is 0.002 cm, but the assertion claims it is 0.001 cm.
Therefore, Assertion (A) is incorrect.
Conclusion:
Reason (R) is a correct statement, but Assertion (A) is an incorrect statement. This matches option (D).