Chapter 1 — Measurement: Foundation of Science

1. Meaning of measurement

Measurement is the comparison of an unknown physical quantity with a known standard quantity of the same kind.

A measurement consists of:

Physical quantity = Numerical value × Unit

For example, if the length of a table is 2 m, then 2 is the numerical value and metre is the unit.

An important idea is that changing the unit does not change the actual physical quantity. It only changes its numerical representation.$$Q=n_1u_1=n_2u_2$$

Therefore,$$n_2=n_1\frac{u_1}{u_2}$$

A larger unit gives a smaller numerical value, while a smaller unit gives a larger numerical value.

2. Systems of units

The chapter introduces three important systems:

System	Length	Mass	Time
CGS	centimetre	gram	second
FPS	foot	pound	second
MKS	metre	kilogram	second

The MKS system eventually developed into the SI system.

3. SI system

The SI system is the internationally accepted system of measurement.

Important base units are:

• Length → metre (m)
• Mass → kilogram (kg)
• Time → second (s)
• Temperature → kelvin (K)
• Electric current → ampere (A)
• Luminous intensity → candela (cd)
• Amount of substance → mole (mol)

The SI system is useful because it is internationally accepted and follows a decimal structure.

4. Unit conversion

Conversion changes the numerical value and unit but preserves the physical quantity.

Important conversions:$$1\,km=1000\,m$$$$1\,m=100\,cm$$$$1\,kg=1000\,g$$$$1\,h=3600\,s$$

For example:$$9\,km/h=9\times\frac{1000}{3600} =\frac52\,m/s$$

Key idea

A unit is not merely a label—it establishes the scale against which a quantity is compared.

The chapter also uses simple measurement activities to show why standard units are necessary and how estimation can be compared with actual measurement.

Chapter 1 — Measurement: The Foundation of Science

Questions

A. Multiple Choice Questions

1. Measurement of a physical quantity requires comparison with:
a) An arbitrary number
b) A standard unit
c) Another unrelated quantity
d) A measuring instrument only

2. Which of the following is an SI base unit?
a) Centimetre
b) Gram
c) Kilogram
d) Hour

3. Which system uses centimetre, gram and second as its fundamental units?
a) MKS
b) CGS
c) FPS
d) SI

4. If a smaller unit is selected for measuring the same physical quantity, the numerical value of the measurement will generally:
a) Increase
b) Decrease
c) Become zero
d) Remain unchanged

5. Which of the following is not an SI base unit?
a) Metre
b) Second
c) Kelvin
d) Foot

6. The SI unit of luminous intensity is:
a) Mole
b) Candela
c) Ampere
d) Kelvin

7. The SI unit of amount of substance is:
a) Mole
b) Kilogram
c) Candela
d) Newton

8. $9\,km/h$ is equal to:
a) $2.5\,m/s$
b) $9\,m/s$
c) $25\,m/s$
d) $0.4\,m/s$

B. Fill in the Blanks

9. Measurement is the comparison of an unknown quantity with a ______ standard.

10. The SI unit of length is the ______.

11. The SI unit of time is the ______.

12. One kilometre contains ______ metres.

13. One kilogram contains ______ grams.

14. One hour contains ______ seconds.

C. State True or False

15. Changing the unit changes the actual physical quantity.

16. SI provides a common international system of measurement.

17. Kilogram is an SI base unit.

18. Foot is an SI base unit.

D. Very Short Answer Questions

19. What is meant by a physical quantity?

20. Why are standard units needed?

21. Write the relationship between magnitude, numerical value and unit.

22. Name three systems of units.

E. Numerical Questions

23. Convert $250\,N$ into $g\,cm/s^2$.

24. Convert $1000\,kg/L$ into $kg/m^3$.

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Answers

A. MCQ Answers

1. b) A standard unit
2. c) Kilogram
3. b) CGS
4. a) Increase
5. d) Foot
6. b) Candela
7. a) Mole
8. a) 2.5 m/s2.5\,m/s

B. Fill in the Blanks

9. known
10. metre
11. second
12. 1000
13. 1000
14. 3600

C. True/False

15. False
16. True
17. True
18. False

D. Answers

19. A physical quantity is a measurable property that can be expressed by a numerical value and a unit.
20. Standard units provide a common basis for accurate comparison and communication of measurements.

$$\text{Magnitude}=\text{Numerical value}\times\text{Unit}$$

22. CGS, MKS and FPS.

E. Numerical Answers

23. Since

$$1N=10^5\,g\,cm/s^2$$

therefore,$$250N=250\times10^5$$$$\boxed{2.5\times10^7\,g\,cm/s^2}$$

24. Since

$$1L=10^{-3}m^3$$$$1000\,kg/L =1000\times1000\,kg/m^3$$$$\boxed{10^6\,kg/m^3}$$

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