# Screw Gauge Experiment

Experiment: Determine the diameter of a given wire using a screw gauge.

Pitch: The pitch of the screw is the distance through which the screw moves along the main scale in one complete rotation of the cap on which is engraved the circular scale.

Least Count: The least count of the screw gauge is the distance through which the screw moves when the cap is rotated through one division on the circular scale.

Zero error and correction: When the zero mark of the circular scale and the main scale do not coincide on bringing the studs in contact the instrument has zero error. The zero of the circular scale may be in advance or behind the zero of the main scale by a certain number of divisions on circular scale. If the zero of the circular scale is ahead of the zero of main scale the zero error is negative. On the other hand if the zero of the circular scale is behind the zero of the pitch scale, the zero error is positive.

Back-lash error: Owing to ill fitting or wear between the screws and the nut, there is generally some space for the play of the screw, the screw may not move along the its axis for appreciable rotation of the head (or cap, on which circular scale is marked). The error so introduced is called back-lash errors. To eliminate it you must advance the screw, holding it by the ratched cap, when making final adjustment for finding zero error or the diameter of the wire.

Material Required

Given wire, screw gauge

### How To Perform Experiment

1. Measuring pitch: To measure the pitch give several rotation to its cap and observe the distance through which screw moves. Calculate the pitch using the following formula:

Pitch = distance moved / No. of complete rotations

2. Measuring least count: To measure the least count note the number of divisions on the circular scale and calculate

Least count (L.C.) = Pitch of the screw / No. of divisions on the circular scale

3. Measuring zero error: With the studs in contact observe the numbers of divisions by which zero of the circular scale deviates from the zero of the main scale. This number multiplied by the least count gives the required zero error.

4. Calculate the zero correction: It is negative of zero error.

Zero correction = – (zero error)

Zero correction is added algebraically in the observed diameter of wire to get the corrected reading.

5. Measuring diameter: To measure the diameter of the wire move the screw back to make a gap between the studs. Insert the wire between the studs. Turn the screw forward by holding it from the ratchet cap and wire should be held gently between the two studs.

6. Read the neaerest division on the circular scale in line with the main scale and also find the complete rotations of the cap with the help of the main scale. Calculate the observed diameter:

Observed diameter = pitch × number of complete rotation + L.C. × circular scale reading

7. Repeat the experiment for 5 observations at different points of the wire along its length. Find the mean observed diameter and apply the zero correction to obtain correct diameter.

### Sources of Errors

1. If the instrument be screwed up tightly when finding zero error or taking reading of diameter of wire (perhaps on account of defective on hard ratchet cap) it may compress the wire out of shape.
2. If the screw is not turned by holding the ratchet cap then the screw may compress the wire out of shape.
3. To eliminate the back-lash error, the screw should always be turned in the same direction (i.e. in forward direction) when making the final adjustment. Negligence of this procedure can come a major error.