**To derive a formula of pitch of a screw:**

The distance covered by the screw when its head makes a complete rotation = 1 × pitch of the screw.

The distance covered by the screw when its head makes 10 complete rotations = 10 × pitch of the screw

The distance covered by the screw when its head makes 'n' complete rotations (x) = n × pitch of the screw

Pitch of the screw = The distance covered by the screw (x) /No. of complete rotations

made by the head (n).

**To derive a formula for the least count of a screw gauge:**

The distance covered by the screw when its head makes a complete rotation

= 1 × pitch of the screw

The distance covered by the screw when its head makes 1/10 of a complete rotation

= 1/10 × pitch of the screw.

Out of N divisions of the head scale, if only one division crosses the index line then the head of the screw makes 1/N of a complete rotation.

The distance covered by the screw when its head makes 1/N of a complete rotation

= 1/N × pitch of the screw

This distance is the smallest distance that can be measured accurately, by the screw gauge when the head contains N divisions on it. So this can be considered as the least count of the screw gauge.

Generally the L.C. of a screw gauge will be 0.01 mm or 0.001 cm. So it is also known as micrometer screw gauge.

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