Question

$\text{Assertion A}$ : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is $5\text{mm}$ and there are $50$ total divisions on circular scale, then least count is $0.001\text{cm}$.

$\text{Reason R}$ :
$\text{Least Count}=\frac{\text{Pitch}}{\text{Total divisions on circular scale}}$

In the light of the above statements, choose the most appropriate answer from the options given below :

• A. $\text{A}$ is not correct but $\text{R}$ is correct.
• B. Both $\text{A}$ and $\text{R}$ are correct and $\text{R}$ is the correct explanation of $\text{A}$.
• C. $\text{A}$ is correct but $\text{R}$ is not correct.
• D. Both $\text{A}$ and $\text{R}$ are correct and $\text{R}$ is NOT the correct explanation of $\text{A}$.

Answer 1

The correct option is A $\text{A}$ is not correct but $\text{R}$ is correct.

For the screw gauge, the least count $\left(\text{LC}\right)$ is given by the following formula,

$\text{Least Count}=\frac{\text{Pitch}}{\text{total division on circular scale}}$

In $5$ revolution, distance travel, $5\text{mm}$

So, $1$ revolution, it will travel $1\text{mm}$.

Therefore, least count of screw gauge will be,

$\text{LC}=\frac{1}{50}=0.02\text{mm}=0.002\text{cm}$

It means the mentioned reason is correct, but the assertion is incorrect for the same.

Therefore option $\left(\text{A}\right)$ is correct.