Measuring Instruments

What are the Measuring Instruments?

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Some Common Measuring Instruments

 

  1. The measuring tape is used to measure lengths of several meters. Measurements are accurate up to 0.01 m. It is suitable for measuring the distance jumped by a long jumper, the distance of the throw of a javelin and the height of a jump by a high jumper.
    What are the Measuring Instruments 1
  2. The meter rule is used to measure lengths of a few centimeters to a meter. Measurements are accurate up to 0.1 cm. It can be used to measure the length of a pencil, the width of a book and the height of a school bag.
    What are the Measuring Instruments 1a
  3. The vernier callipers is used to measure lengths of less than 10 cm. Measurements are accurate up to 0.01 cm. It can be used to measure the external and internal diameters of round objects like pipes and cylindrical containers. It can also measure the thickness of a book, a piece of glass pane and even the width of a crack.
    What are the Measuring Instruments 2
  4. The micrometer screw gauge is used for very small readings. Measurements are accurate up to 0.01 mm. It can be used to measure the thickness of a cardboard, a coin or a key and the diameter of a piece of wire.
    What are the Measuring Instruments 3

Reading the Vernier Callipers

Example 1. Figure shows a pair of vernier callipers being used to measure the diameter of a metal pipe.
What are the Measuring Instruments 4Solution:
Reading on main scale = 2.1 cm
Reading on the vernier scale = 0.07 cm
Therefore, the diameter of the metal pipe = 2.1 + 0.07
= 2.17 cm

Example 2. A boy uses a pair of vernier callipers to measure the width of a handphone as shown in Figure.
What are the Measuring Instruments 5What is the reading of the vernier callipers?
Solution:
Reading on main scale = 4.0 cm
Reading on the vernier scale = 0.04 cm
Therefore, the width of the handphone = 4.0 + 0.04 = 4.04 cm

Zero Errors in Vernier Callipers

What are the Measuring Instruments 6Above Figure shows three possible situations when using a pair of vernier callipers, that is,
(a) no zero error,
(b) positive zero error,
(c) negative zero error.
Hence,
Correct reading = Reading obtained – Zero error
What are the Measuring Instruments 7

Example 3. Figure shows a pair of vernier callipers with zero error being used to measure the thickness of a book.
What are the Measuring Instruments 8What is the thickness of the book?
Solution:
Zero error = +0.03 cm
Reading with zero error = 1.99 cm
Therefore, the thickness of the book
= 1.99 – 0.03
= 1.96 cm

Example 4. Figure shows a pair of vernier callipers with zero error being used to measure the width of a remote control.
What are the Measuring Instruments 9
What are the Measuring Instruments 10What is the width of the remote control?
Solution:
Negative zero error is involved. Hence, the reading cannot be made directly.
Zero error = -(0.63 – 0.6)
= -0.03 cm
What are the Measuring Instruments 11
Reading with zero error = 5.26 cm
Therefore, the width of the remote control = 5.26 – (-0.03)
= 5.29 cm

Example 5. The diagram shows the position of a vernier scale at the main scale of a vernier calipers. What is the value of s?
What are the Measuring Instruments 12Solution:
The reading of the measurement is 5.16 cm.
Hence s = 0.16 cm.

Reading the Micrometer Screw Gauge

Example 6. Figure shows a micrometer screw gauge being used to measure the thickness of a coin.
What are the Measuring Instruments 13What is the thickness of the coin?
Solution:
Reading on the main scale = 2.50 mm
Reading on the thimble scale = 0.27 mm
Thickness of the coin = (2.50 + 0.27) mm
= 2.77 mm

Example 7. Figure shows the scale of a micrometer screw gauge.
What are the Measuring Instruments 14What is the reading of the micrometer?
Solution:
Reading on the main scale = 5.50 mm
Reading on the thimble scale = 0.33 mm
Therefore, the reading of the micrometer = 5.50 + 0.33
= 5.83 mm

Zero Errors in Micrometer Screw Gauge

There are two possible types of zero errors in using the micrometer screw gauge, that is the positive zero error and the negative zero error.
What are the Measuring Instruments 15

Example 8. Figure (a) shows the zero error of a micrometer screw gauge and Figure (b) shows its subsequent reading of a measurement.
What are the Measuring Instruments 16What is the actual value of the measurement?
Solution:
Zero error = +0.01 mm Reading = 4.29 mm
Actual value of measurement = 4.29 – 0.01
= 4.28 mm

Example 9. Figure (a) shows the zero error of a micrometer screw gauge and Figure (b) shows its subsequent reading of a measurement.
What are the Measuring Instruments 17What is the actual value of the measurement?
Solution:
Zero error = -0.01 mm
Reading = 6.30 mm
Actual value of measurement = 6.30 – (-0.01)
= 6.31 mm

Understanding Measurements

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Understanding Measurements

 

  1. Physics is based on measurements. Experiments which are the key to the development of physical theories involve measurements of various physical quantities.
  2. Various measuring instruments are used for different types of measurements and the reading obtained by each instrument must be presented in suitable units.
  3. Choosing an appropriate instrument to measure a physical quantity is important to ensure that the measurement is accurate and reproducible.
  4. Consistency, accuracy and sensitivity are three important aspects of a measurement.

Consistency and Accuracy

  1. No measurement is exact. Every measurement is an estimation of the actual value. For example, even the most accurate clock used in the Olympics does not give the exact time of a 100 m runner. It only gives an accurate estimate of the actual time.
    Understanding Measurements 1
  2. Consistency and accuracy are two important properties of measurements. Consider a target as in Figure.
    (a) The bullseye in the centre of the target represents the actual or true value of the quantity to be measured.
    (b) Individual measurements of the quantity under identical conditions are represented schematically by individual shots taken by the marksman on the target.

    Understanding Measurements 2
    Fig. Consistency

    (c) When the shots are closely clustered together, it shows that repeated measurements yield almost the same reading. We say that the measurements are consistent. Consistency of an instrument is the ability of the instrument to measure a quantity with little or no deviation among measurements.
    Language support:
    Deviation means the difference between the measured value and its mean value.

    Understanding Measurements 3
    Fig. Accuracy

    (d) The nearer a shot is to the bullseye, the nearer is the measurement to the actual value. We say that the measurement is accurate. Accuracy of a measurement is how close the measurement made to the actual value.

Example 1. Figure shows four sets of measurements on boards A, B, C and D each of which represent a rifle target.Understanding Measurements 4
(a) Comment on the consistency and accuracy of the measurements of boards A, B and C.
(b) Suggest one possible reason for the set of measurements shown on board D.
Solution:
(a) Board A – Consistent and accurate
Board B – Consistent but not accurate
Board C – Not consistent and not accurate
(b) Three measurements are accurate and consistent. The other measurement may be due to a wrong reading.

Example 2. Instrument X and instrument Y are used to measure the thickness of a dictionary. Table shows two sets of readings taken by the respective instruments.Understanding Measurements 5Which of the two instruments is more consistent? Explain your answer.
Solution:
Instrument X is more consistent. This is because the measurements taken by instrument X are closer to each other (or there is little deviation between the measurements).

Sensitivity of Measuring Instruments

  1. Sensitivity of a measuring instrument is its ability to detect quickly a small change in the value of quantity to be measured.
  2. The smaller the minimum scale division of a measuring instrument, the more sensitive is the instrument.
  3. Table shows the sensitivity of some common instruments for measuring length.
    Understanding Measurements 6

Example 3. A hawker has two measuring scales, A and B. A has a measuring range of 0 – 400 g and gives the smallest reading of 10 g or 0.01 kg. B has a measuring range of 0 – 4 kg and gives the smallest reading of 0.1 kg. A lady wants to buy a whole chicken of about 1.5 kg and red chillies of about 200 g.

Understanding Measurements 7State which scale is suitable for each of the items and explain your answer.
Solution:
Scale B is more suitable for measuring a whole chicken because the mass of the chicken is out of the range of measurement of scale A.
Scale A is more suitable for measuring the red chillies because it is more sensitive and can detect small changes in the mass.

Example 4. A, B, C and D show the scales of four different meters respectively. Which meter is the most sensitive?Understanding Measurements 8Answer: A
Meter A has the smallest minimum scale division out of the four meters.

Understanding Measurements 9Voltmeter A is more sensitive than voltmeter B because:

  1. Volmeter A has a smaller minimum scale division compared to voltmeter B.
  2. Voltmeter A can detect a smaller change in the voltage than voltmeter B.
  3. For the same variation of voltage, voltmeter A gives a bigger deflection than voltmeter B.