A Screw Gauge gives the following readings when used to measure the diameter of a wire.
Main scale reading = $

Question

A Screw Gauge gives the following readings when used to measure the diameter of a wire.
Main scale reading = $0.0	ext{ mm}$
Circular scale reading = $52	ext{ divisions}$
Given that: $1	ext{ mm}$ on the main scale corresponds to $100	ext{ divisions}$ of the circular scale. The diameter of the wire from the above data is:

Accepted Answer

1. **Determine the Least Count (LC):** The pitch of the screw gauge is given as $1	ext{ mm}$, and the total number of divisions on the circular scale is $100$. The least count is calculated as $	ext{LC} = \frac{	ext{Pitch}}{	ext{Total circular divisions}} = \frac{1	ext{ mm}}{100} = 0.01	ext{ mm}$.
2. **Calculate the Total Reading:** The formula for the measurement is $	ext{Total Reading} = 	ext{Main Scale Reading (MSR)} + (	ext{Circular Scale Reading (CSR)} 	imes 	ext{LC})$.
3. **Substitute the Values:** $	ext{Total Reading} = 0.0	ext{ mm} + (52 	imes 0.01	ext{ mm}) = 0.52	ext{ mm}$.
4. **Convert Units:** The options are given in centimeters. To convert millimeters to centimeters, divide by $10$. Therefore, the diameter of the wire is $0.52	ext{ mm} = 0.052	ext{ cm}$.

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