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Physical Quantities And Measurement

Length: Ruler, Vernier caliper and screw gauge

Physics

Formulas / Equations

Length = Final Point - Initial Point

Final Reading of a Vernier Caliper = Main scale Reading + Vernier Reading

Final Reading of a Screw gauge = Sleeve reading + Thimble Reading

Corrected Reading = Observed Reading – Zero Error

Key Concepts

Length:

The length is defined as the minimum distance between two points lying on the same plane. The SI unit of length is meter (m).

Standard of Length:

The length of the path traveled by light in vacuum during the time interval of 1299792458th\frac {1}{299 792 458} th of a second.

Ruler, Vernier caliper and screw gauge are some of the instruments used to measure length.

VERNIER CALIPER:

The ‘Vernier Caliper’ is a precision instrument that can be used to measure internal and external distance extremely accurate. Vernier caliper has main jaws that are used for measuring external diameter, as well as smaller jaws that are used for measuring the internal diameter of objects.

READING THE VERNIER CALIPER:

To read the measurement of a Vernier Caliper, we need to take two readings:

  1. Main scale reading: To obtain the main scale reading, look at the image above, 3.1 cm is to the immediate left of the zero on the Vernier scale. Hence, the main scale reading is 3.1 cm

  2. Vernier scale reading: To obtain the Vernier scale reading, Look at the image above and look closely for an alignment of the scale lines of the main scale and Vernier scale. In the image above, the first aligned line correspond to 4. Hence, the Vernier scale reading is 0.4 mm or 0.04 cm.

  3. Final measurement reading: In order to obtain the final measurement reading, we will add the main scale reading and Vernier scale reading together. This will give 3.1 cm + 0.04 cm = 3.14 cm.

Final reading = Main scale reading + Vernier scale reading

Zero Error: Is a type of error in which an instrument gives a reading when the true reading at that time is zero.

Zero error in Vernier Calipers:

• Zero Errors can of two types: Positive and Negative.

• Positive Zero error is when the Vernier zero is to the right of the Main Scale zero.

• Negative Zero error is when the Vernier zero is to the left of the Main Scale zero.

• In both cases the Corrected Reading = Observed Reading – Zero Error

MICROMETER SCREW GAUGE:

A micrometer screw gauge is used for measuring extremely small lengths. It is extensively used in the engineering field for obtaining precision measurements.

READING A MICROMETER SCREW GUAGE:

To read the screw gauge, you need to take two readings:

  1. Sleeve Reading: To obtain the first part of the measurement: Look at the image above, you will see that the 4th mark above the datum is to the immediate left of the thimble. This means 4.0 mm. Notice that there is an extra line below the datum line, this represents an additional 0.5 mm. So the first part of the measurement is 4.0+0.5=4.5 mm.

  2. Thimble Scale Reading: Look at the image above, the 12th mark on the rotating Vernier scale coincides with the datum line on the sleeve. Hence 0.12 mm is the second part of the measurement.

  3. Final reading: In order to obtain the final measurement reading, we will add the sleeve scale reading and thimble scale reading together. This will give 4.5 mm + 0.12 cm = 4.62 cm.

Final Reading= Sleeve Reading + Thimble Scale Reading

Zero error in screw gauges:

• Positive Zero Error is when the Thimble Zero is below the Datum Line.

• Negative Zero Error is when the Thimble Zero is below the Datum Line.

• Zero error is counted from the Thimble Zero to the Datum Line in both cases.

• In both cases the Corrected Reading = Observed Reading – Zero Error

UNIT CONVERSION OF LENGTH: