 # Measurement of Length

## •    Different instruments such as a metre scale, vernier callipers and a screw gauge can be used to measure length of different objects. For correct measurement of length, few important steps are to choose correct instrument, correct placement of the scale, and  while finding the measurement, eyes should be exactly in front of the mark of the point from where the measurement is to be taken and it should also be parallel to the surface.                                                                            Vernier Callipers •    Vernier callipers are used to measure length, thickness, depth and internal and external diameter of an object. Least count and zero error of the vernier callipers should be known before making measurements with vernier callipers.                                                                             Screw Gauge •    A screw gauge is an instrument generally used to measure the diameter of thin wires, thickness of sheets and even to find the volume of irregular lamina. Every measuring instrument has a least count and zero error. •    Least count of a device is the smallest measurement that can noted using it. •    Zero error is an instrumental error. In case of vernier callipers, zero error occurs when a zero on main scale does not coincide with a zero on vernier scale. The zero error may be of two types Positive zero error: Positive zero error occurs when the zero of the vernier scale is on the right of zero of the main scale zero and the zero correction will be negative. Negative zero error:  Negative zero error occurs when the zero of the vernier scale is on the left of the main scale zero and zero correction will be positive. •    Screw gauge also have positive and negative zero errors.

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• Q1

Calculate the least count of the given vernier callipers.

Marks:2

• Q2

A screw gauge has a positive error of 2 divisions. If the diameter of a thin wire using the screw gauge comes out to be 1.06 mm, then find its correct diameter.

The least count of the screw gauge is 0.01 mm.

Marks:2

Positive zero error = number of coinciding divisions x least count

= + (2 x 0.01) mm = 0.02 mm

The correct reading of diameter can be given by,

=1.06 mm – (+ 0.02 mm)

= 1.06 mm – 0.02 mm

= 1.04 mm

• Q3

Calculate the length of the cube in the shown figure.

Marks:1

Given,

Initial point = 2 cm

Final point = 14 cm

Length = final point – initial point

= 14 cm – 2 cm = 12 cm

• Q4

Name a device most appropriate to measure

(a) height of a person

(b) length of a cloth piece

Marks:1

(a) Height of a person should be measured using a measuring tape.

(b) Length of the clothe piece should be measured using a metre rule.