To Measure The Diameter Of A Given Wire Using Screw Gauge

The screw gauge is an instrument for precisely measuring the diameter of a thin wire or the thickness of a metal sheet.

• It consists of up of a U-shaped frame with a screwed spindle attached to a thimble. 
• A screw gauge contains two scales, known as the Pitch scale and the Circular scale. 
• The main scale is the pitch scale, which is carved on the barrel with vertical lines. 
• The Circular Scale, which is engraved horizontally on the thimble. The pitch scale measures the distance traveled by the spindle every revolution in millimeters (mm). 
• A micrometer screw gauge is one rotation on a circular scale equivalent to half a millimeter of screw displacement. 
• Micrometre gauges are more precise and accurate than the Vernier Calliper scale. 
• The Least count (LC) is the distance traveled by the screw tip when it is rotated through one division of the head scale.

Key Terms: Screw gauge, Least count, Zero error, Micrometer, Pitch, Main scale, Magnifying glass

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Aim

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To measure the diameter of a given wire using a screw gauge.

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Apparatus Required

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The materials/apparatus required to perform this experiment are

• Screw gauge
• Half-meter scale
• Wire
• Magnifying glass

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Theory

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A screw gauge is a precision measuring instrument used to measure the diameter of thin wires and the thickness of small sheets. 

• It works on the principle of a screw and nut mechanism. 
• The screw gauge consists of a U-shaped frame with a fixed anvil at one end and a movable spindle at the other end. 
• The spindle is attached to a thimble, which is graduated into 50 or 100 divisions. The frame is also graduated into millimeters and half-millimeters.
• To measure the diameter of a wire or the thickness of a sheet, the object is placed between the anvil and the spindle. 
• The thimble is then turned until the spindle just touches the object. 
• The reading on the thimble is then added to the reading on the frame to give the overall measurement.

Least Count

The least count of a measuring instrument is the smallest value that can be accurately measured with that instrument. It is typically calculated by dividing the smallest division on the instrument's scale by the number of divisions.

• Any measurement made by the instrument can be considered repeatable to no less than the resolution of the least count. 
• The least count of an instrument is inversely proportional to the precision of the instrument.

Calculation of Least Count

The least count of a screw gauge is given by

If a screw gauge has a pitch of 1 mm and 100 divisions on the circular scale then the least count is given as

LC = = 0.01 mm

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Diagram

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Screw gauge measuring the diameter of the wire

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Procedure

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The following is the procedure to measure the diameter of a given wire using a Screw gauge

• Step 1: Determine the value of a single linear scale division (L.S.D.).
• Step 2: Determine and record the least count and pitch of the screw gauge.
• Step 3: Bring the plane faces B and A close together to obtain the zero error. This should be done three times. If there is no error, record zero error as nil.
• Step 4: Face B should be moved away from face A. Move the face A towards the face B lengthwise with a ratchet head R and stop when R rotates without moving the screw.
• Step 5: Linear scale reading (L.S.R.) can be measured by recording the number of visible and uncovered linear scale divisions.
• Step 6: Let n be the number of divisions of the circular scale on the reference line.
• Step 7: Repeat steps 5 and 6 by turning the wire 90° to measure diameter in a perpendicular direction.
• Step 8: Repeat procedures 4, 5, 6, and 7 for five different points along the whole length of the wire and note your results.
• Step 9: Determine the total reading as well as the zero correction.
• Step 10: Take the average of the different diameter values.
• Step 11: Measure the length of the wire on a half-meter scale. Repeat this procedure three times, and record the results.

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Observations

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The following are the observations of the experiment

1. For the determination of the least count of screw gauge, we have

Linear scale division, L.S.D = 1 mm

The number of full rotations given to the screw = 4 

Hence, the distance moved by the screw = 4 mm

Therefore, the pitch of the screw gauge = (4 mm)/4 = 1 mm

Number of divisions on a circular scale = 100

Least Count = (1 mm)/100 = 0.01 m = 0.001 cm

2. Zero error: (i)...… mm, (ii)...…. mm, and (iii)……... mm

Mean zero error: (e) =…… mm 

Mean zero correction: (C) = -e -…….. mm

3. Table for diameter (D)

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Calculations

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Length of the wire, l = (i)…..cm (ii)…..cm (iii)…..cm

Mean corrected internal diameter

D = = .......... cm

The mean length of the wire

L = = .......... cm

The volume of the wire

V =  = .......... cm

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Result

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The volume of the given wire is ………cm³

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Precautions

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The following precautions should be taken while performing the experiment

• When rotating the screw, there should be no friction.
• To minimize unnecessary pressure, the screw should always be turned by ratchet R rather than cap K.
• The proper sign should be specified for zero correction.
• The screw should be pushed in the same direction to avoid backlash errors.
• The diameter of the wire should be measured in two perpendicular directions at each location, and the mean should be calculated.
• Readings should be obtained at five different places throughout the whole length of the wire.
• Parallax errors should be avoided.

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Sources of Error

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The errors can be introduced in the measurement due to the following reasons

• The screw gauge may have a backlash error.
• There might be friction in the screw
• Circular scale divisions may not be divided equally.
• The wire may not be uniformly distributed.

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Things to Remember

• Measuring tools are tools used to measure physical body quantities such as height, width, length, temperature, and so on.
• A screw gauge measures the diameter of a thin wire or the thickness of a metal sheet precisely.
• A screw gauge contains two scales, known as the Pitch scale and the Circular scale.
• When measuring instruments are used, the least count is the smallest value that can be determined.
• The least count of the screw gauge is 0.001 cm
• Zero error occurs when a measurement device records a measurement when no reading is required.

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