Units And Measurements

In this article, we will learn about the following topics as per the syllabus of the Secondary 3 Physics.

• Physical Quantities
• Units and Prefixes

What is Physics?

Physics is the study of matter and energy, and the interaction between the two.

Physical Quantities

• A physical quantity is a quantity that can be measured. 
• It consists of a numerical magnitude and a unit.

For example: 

In the case of 35 cm

• 35 is the numerical magnitude. 
• cm is the unit. 

Practice Questions

Question 1:

Which of the following is/are not physical quantities?

1. Money
2. Happiness
3. Time
4. Pain

1. 2 only
2. 2 and 4 only
3. 1, 2 and 4
4. None of the above

Solution:

Option B is the correct option.

Explanation:

Money is a physical quantity as it can be measured. Our bank account tells us how much money we have.

Happiness is NOT a physical quantity as it is a subjective matter. We cannot use any measuring instrument to measure the happiness of a person. What causes happiness to one person may not be the cause of happiness for the other person. In turn, he may feel sad about it.

Time is a physical quantity. We can check the time using the clock. 

Pain is NOT a physical quantity. It is also subjective in nature. The tolerance level of pain of different people is different. For some, a small prick of a needle can be painful for some people. For others, even a heavy injury is regarded as a minor nuisance.

SI Units

An SI unit is a unit of measurement in the International System of Units.

Almost the whole world uses the same units to measure the physical quantities.

So, why do we need this system of units?

The aim of this system is to promote common understanding among scientists and merchants around the world.

Question 2:

Which of the following does not have an SI unit?

1. Money
2. Weight
3. Time
4. Temperature

1. 1 only
2. 2 only
3. 2, 3 and 4
4. None of the above

Solution:

Option A is the correct answer.

Explanation:

Money does not have an SI unit. Each country has its own currency. For example, in India we use Indian Rupee; in the USA we use American Dollars; in Singapore, we use Singapore Dollars etc.

Base Quantities / Units

Base quantities are a set of independent physical quantities.

All other physical quantities will be derived by the multiplication or division of two or more base quantities.

SI units of the base quantities are called base units. Non SI units are NOT to be considered as base units.

Question 3: 

Which of the following is NOT a base quantity?

1. Time
2. Weight
3. Length
4. Current

Solution: 

Option B is the correct answer.

Explanation:

Weight is not a base quantity even though mass is a base quantity. In physics, weight and mass are different quantities even though they are related. 

Time, length and current are all base quantities.


Question 4:

Which of the following is a base unit?

1. centimetre
2. grams
3. second
4. volts

Solution:

Option C is the correct answer

Explanation:

Centimetre is NOT a base unit even though it is a unit for length. But since centimetre is NOT a SI unit, it cannot be considered as a base unit.

Grams is NOT a base unit even though it is a unit for mass. But since grams is NOT a SI unit, it cannot be considered a base unit.

Second is a base unit of time and it is also a SI unit.

Volts is NOT a base unit even though it is the SI unit for voltage. Voltage is not a base quantity, that is why volts is not a base unit.

Derived Quantities

A derived quantity is given by the multiplication or division of two or more base quantities.

The unit of a derived quantity is given by the multiplication or division of the corresponding base units.

Let us take an example:

\(Speed = \frac {distance}{time}\) 

Speed is not a base quantity. It is calculated by the above formula. So, what about the units of speed?

The units of all the derived quantities can be calculated or worked out by some combination of base units.

Unit of speed = SI unit of distance /  SI unit of time

Unit of speed = \(\frac {meter}{second}\)

Unit of speed = m s^–1 or m/s

Let us consider another example -

Volume of a cuboid = length × width ×  height

Unit of volume =  m × m × m

Unit of volume = m³

Thus, we see how we can work out the units of derived quantities by using base units.

Question 5: 

Which of the following is a possible unit for kinetic energy?

( Kinetic energy = \(\frac 1 2\) × mass × speed² )

1. kg m s^–1
2. kg² m² s^–2
3. kg m² s^–2
4. kg m² s²

Solution: 

Option C is the correct answer

Explanation:

The constant \(\frac 1 2\) has no units.

Mass has a base unit of kg.

Speed has the unit of m s^–1.

Thus, the unit of kinetic energy is as follows

Unit if kinetic energy = kg × (m s^–1)² = kg m² s^–2

Multiples And Submultiples (Prefixes)

The magnitudes of physical quantities can range from very big to very small.

The mass of a truck can be 5000000 g.

The width of your hair strand is about 0.00007 m.

Writing so many zeros -

1. Is inconvenient.
2. Carries a greater risk of miscounting the number of zeroes.

So, prefixes are used to denote the multiples or submultiples of an SI unit.

Conclusion

In this article, we learned about the following topics:

• Physical Quantities

We have learnt what are the physical quantities, the base quantities, and the derived quantities.

• Units and Prefixes

Under this topic, we have learnt the units of the base quantities, the SI units of the base quantities, the non-base units, the units for derived quantities, and the prefixes used for the multiples and submultiples of the SI unit.