Question

When a screw gauge with a least count of $0.01mm$ is used to measure the diameter of a wire, the reading on the sleeve is found to be $1mm$ and the reading on the thimble is found to be $27$ divisions. What is the diameter of the wire in $cm$?
$A)\text{ }0.127cm$
$B)\text{ }0.127mm$
$C)\text{ }1.27cm$
$D)\text{ }0.027cm$

Answer 1

This problem can be solved by using the direct formula for the reading obtained by a screw gauge in terms of the linear scale reading, the circular scale reading and the least count of the screw gauge. The reading on the sleeve is the main scale reading while the reading on the thimble is the circular scale reading.
Formula used:
$\text{Reading = Linear Scale Reading + }\left( \text{Least count}\times \text{Circular Scale Reading} \right)$

Complete answer:
We will use the formula for the measurement value of the reading of a screw gauge in terms of the linear scale reading, the circular scale reading and the least count of the screw gauge.
The value of the measurement done by the screw gauge is given by
$\text{Reading = Linear Scale Reading + }\left( \text{Least count}\times \text{Circular Scale Reading} \right)$ --(1)
Now, let us analyze the question.
The least count of the screw gauge is given to be $L.C.=0.01mm/\text{division}$.
The linear scale reading is nothing but the sleeve reading. It is equal to $LSR=1mm$.
The circular scale reading is nothing but the thimble reading. It is equal to $CSR=27\text{ divisions}$.
Let the diameter of the wire be $D$.
Therefore, using (1), we get $D$ as
$D=LSR+\left( LC\times CSR \right)$
$\therefore D=1+\left( 0.01\times 27 \right)=1+\left( 0.27 \right)=1.27mm$
$\therefore D=1.27mm=0.127cm$ $\left( \because 1mm=0.1cm \right)$
Therefore, the required value of the diameter of the wire in $cm$ is $0.127cm$.

So, the correct answer is “Option A”.

Note:
Students must know the process of finding out the least count of a screw gauge. The least count of a screw gauge is the ratio of the length of one unit on the linear scale to the number of divisions on the circular scale. The least count gives the value of the smallest length that the screw gauge can measure. Usually, for a screw gauge, the least count is $0.01mm$ but it can be different for some special screw gauges. Students must be thorough with the process of finding out the least count both theoretically and practically. This will also help them while conducting experiments in the labs because for most cases, the least counts are not provided to the students and they are handed with the task of calculating it for their instrument.