Measurement Of Length

SI unit for length is metre (m). It is a scalar quantity.

Things you need to know:

• Accuracy refers to the maximum error encountered when a particular observation is made.
• Error in measurement is normally one-half the magnitude of the smallest scale reading.
• Because one has to align one end of the rule or device to the starting point of the measurement, the appropriate error is thus twice that of the smallest scale reading.
• Error is usually expressed in at most 1 or 2 significant figures.

Tape

Equipment: It is made up of a long flexible tape and can measure objects or places up to 10 – 50 m in length. It has markings similar to that of the rigid rule. The smallest marking could be as small as 0.1 cm or could be as large as 0.5 cm or even 1 cm.

How to use: The zero-mark of the measuring tape is first aligned flat to one end of the object and the tape is stretched taut to the other end, the reading is taken where the other end of the object meets the tape.

Accuracy: ± 0.1 to 1 cm

Rule

Equipment: It is made up of a long rigid piece of wood or steel and can measure objects up to 100 cm in length. The smallest marking is usually 0.1 cm.

How to use: The zero-end of the rule is first aligned flat with one end of the object and the reading is taken where the other end of the object meets the rule.

Accuracy: ± 0.1 cm

Vernier Caliper

Equipment: It is made up of a main scale and a vernier scale and can usually measure objects up to 15 cm in length. The smallest marking is usually 0.1 cm on the main scale.

It has:

• a pair of external jaws to measure external diameters
• a pair of internal jaws to measure internal diameters
• a long rod to measure depths

How to use: The jaws are first closed to find any zero errors. The jaws are then opened to fit the object firmly and the reading is then taken.

Accuracy: ± 0.01 cm

Note: Check out How To Read A Vernier Caliper to learn how to read a vernier caliper.

Micrometer Screw Gauge

Equipment: It is made up of a main scale and a thimble scale and can measure objects up to 5 cm in length. The smallest marking is usually 1 mm on the main scale (sleeve) and 0.01 mm on the thimble scale (thimble). The thimble has a total of 50 markings representing 0.50 mm.

It has:

• an anvil and a spindle to hold the object
• a ratchet on the thimble for accurate tightening (prevent over-tightening)

How to use: The spindle is first closed on the anvil to find any zero errors ( use the ratchet for careful tightening). The spindle is then opened to fit the object firmly (use the ratchet for careful tightening) and the reading is then taken.

Accuracy: ± 0.01 mm

 Note: Check out How To Read A Micrometer Screw Gauge to learn how to read a micrometer screw gauge.

Summary

The choice of measuring equipment depends on the degree of accuracy required.

Range of length, $l$	Equipment	Accuracy	Example
$l > 100 \, \text{cm}$	Measuring tape	$\pm 0.1 \, \text{cm}$	Circumference of your waist
$5 \, \text{cm} < l < 100 \, \text{cm}$	Metre rule	$\pm 0.1 \, \text{cm}$	Length of your phone
$1 \, \text{cm} < l < 10 \, \text{cm}$	Vernier calipers	$\pm 0.01 \, \text{cm}$	Diameter of beaker
$l < 2 \, \text{cm}$	Micrometer screw gauge	$\pm 0.001 \, \text{cm}$   or $\pm 0.01 \, \text{mm}$	Thickness of a piece of wire