Length is the distance between two points. Length is generally measured in metres.
However it can be measured in other units like kilometers, centimeters, decimetres, etc

Length can be measured using a metre rule, a pair of Calipers or a micrometer screw guage
depending on the distance to be measured.

The metre rule is a measuring instrument used to measure large distances. It is calibrated in Centimeters and millimeters. A meter rule of length 1m is equal to 100 centimeters (cm). On the meter rule each cm is divided further in to 10 divisions which are called millimeters (mm). So, a meter rule can measure up to 1mm or 0.1cm as its reading accuracy. The general uncertainty of a metre rule is half its minimum graduation which is ±0.5 mm or ±0.05 cm.

• Place the meter rule on a clean and flat surface to ensure accurate measurements.
• Always read the measurement at eye level to avoid parallax errors.
• Handle the meter rule carefully by its ends or edges, avoiding direct contact with the measurement markings (graduations).
• Check for any zero errors before starting a measurement and make corrections if needed.
• Avoid bending the meter rule and keep it away from extreme temperature conditions to maintain its accuracy.

Vernier calipers are precision measuring instruments used to measure small lengths with high accuracy. They consist of a main scale and a sliding vernier scale that allows for precise readings to be taken. The main scale is fixed, while the vernier scale can slide along it. The vernier scale has a slightly smaller length than the main scale, and it is divided into smaller units, which correspond to a fraction of the main scale unit. The vernier scale is aligned with the main scale so that their zero points coincide.

The vernier caliper has a reading accuracy of 0.1 mm or 0.01 cm which serves as its least count and an uncertainty of ±0.05 mm. It is used to measure the inner and outer diameter of cylindrical objects like test tube, depth of a beaker or bottle, the thickness of a metre rule, etc.

• Read the main scale: Start by identifying the value of the main scale that aligns with the left zero of the vernier scale.
• Locate the vernier scale line: Find the vernier scale line that perfectly matches or is closest to a main scale line.
• Determine the reading: Note the number of the vernier scale line that lines up with a main scale line. This gives you the fractional part, and when added to the main scale reading, gives the final measurement.
Generally,
Final reading = MSR + (VSR x LC)
Where, MSR = main scale reading
VSR = Vernier scale reading
LC = least count = 0.1mm = 0.01cm

Calculate the final vernier caliper reading in the diagram below

From the diagram above, we need to identify the MSR and VSR
MSR = 4.3cm(the mark that coincides with the vernier zero mark)
VSR = 5 (the mark that aligns closest to the main scale)
LC = 0.01cm
Final vernier reading = MSR + (VSR x LC)
= 4.3 + (5 x 0.01)
= 4.3 + 0.05
final vernier reading = 4.35cm

Calculate the reading of the vernier caliper

From the diagram, MSR = 10cm
VSR = 2 (closest to the main scale)
LC = 0.01cm
Vernier caliper reading = 10 + (2 x 0.01)
=10.02cm

Calculate the Zero error in the vernier caliper

From the diagram, we can see that the vernier scale is placed slightly past the zero mark on the main scale. Hence we will encounter a zero error in the reading. Since it is past the zero mark it is a positive error.
To calculate for this, we use:
Zero error = VSR × LC
VSR = 3
LC = 0.01cm
zero error = 3 x 0.01
= +0.03cm = +0.3mm

A boy uses a vernier callipers to measure the thickness of his pencil. He measures it to be
1.4 mm. If the zero error of vernier callipers is
+ 0.02 cm, what is the correct thickness of pencil?
solution
Correct Vernier reading
= Measured reading - (zero error)
Measured reading = 1.4mm
zero error = +0.02cm = 0.2mm
= 1.4 - (+0.2)
= 1.2mm

A micrometer screw gauge is a precision measuring instrument used to measure small distances with great accuracy. It consists of a U-shaped frame with a thimble at one end and a spindle at the other. The thimble is rotated to move the spindle towards or away from the anvil, allowing the measurement of the object's dimensions. The main scale and the rotating thimble with a graduated scale are used to read the measurement. It has a reading accuracy of 0.01mm or 0.001cm

1. Ensure the micrometer is clean and properly calibrated.
2. Place the object to be measured between the spindle and anvil of the micrometer.
3. Close the thimble gently until it makes light contact with the object.
4. Look at the main scale (the long scale) and note the value to the left of the thimble.
5. Now, observe the markings on the circular sleeve of the thimble and count the number of divisions visible.
6. Each division on the thimble represents a certain value, typically 0.01mm or 0.001mm (depending on the micrometer).
7. Add the value from the main scale and the number of divisions from the thimble to get the final measurement.

Reading = MSR + (Thimble reading x LC)
where LC = 0.01mm or 0.001cm

Calculate the Micrometer screw guage reading in the diagram below

Solution
From the diagram, MSR = 6mm
Thimble reading = 43
LC = 0.01mm
Reading = 6 + (43 x 0.01)
= 6.43mm

Calculate the Micrometer screw guage reading in the diagram below

solution
MSR = 2.5mm
Thimble reading = 35
LC = 0.01mm
Reading = 2.5 + (35 x 0.01)
= 2.85mm

Calculate the vernier caliper scale from the diagram below

Solution
from the diagram, MSR = 3mm
Thimble reading = 9
LC = 0.01mm
Reading = 3 + (9 x 0.01)
= 3.09mm