# NCERT Class 9 Science Notes & Solutions – Scalar & Vector Quantity – Units

## Maths & MCQ of Quantity & Units

### 1. What is physical quantity?

Anything which can be measured is called physical quantity. Generally we classify physical quantity into two groups. These are scalar quantity & vector quantity.

### 2. What is scalar quantity

The quantity which has only magnitude but no direction is scalar quantity. For example – mass, speed, time, volume, temperature etc.

### 3. What is vector quantity?

The quantity which has both magnitude and direction is vector quantity. For example – velocity, acceleration, momentum etc.

### 4. Why do we need unit?

At first we need to be familiar with units of every quantity. If we do not have fixed unit of measurement, then we will not be able to make concept regarding any kind of physical quantity. If the unit of length is not fixed, then you can not express distance, expansion, volume etc. When I say the distance between Kolkata and Delhi is 1600, can you make any concept about 1600? Obviously not. But when I say it is 1600 km, then you can make a concept.

#### 5. What is fundamental unit? Is there any quantity which has no unit?

Generally it has been found that if we fix the units of three quantity, then we can derive units of all other quantities by using units of that three quantities. Specifically these three quantities are – A. Length, B. Mass and C. Time. Basically units of these three quantity are independent and not related to each other. So units of these three quantity are called fundamental unit. Therefore,  using these fundamental unit, you can derive unit of other quantities. For example – unit of length is metre. So if you want unit of speed, then it is metre/second. Other examples are area (metre2), volume (metre3 ), acceleration (metre/second2) etc.

Quantity without unit: For example –  Relative Density, Atomic Density etc.

#### 6. Write fundamental units in C.G.S. system.

Generally there are three fundamental quantities. These are– a. Length, b. Mass, c. Time. The C.G.S. unit of these quantities are given in the following –

• C ⇒ Centimetre ⇒ Unit of Length
• G ⇒ Gram ⇒ Unit of Mass
• S ⇒ Second ⇒ Unit of Time

#### 7. Write fundamental units in M.K.S. system.

There are three fundamental quantity i.e. a. Length, b. Mass, c. Time. The M.K.S. unit of these quantities are given in the following –

• M ⇒ Metre ⇒ Unit of Length
• K ⇒ Kilogram ⇒ Unit of Mass
• S ⇒ Second ⇒ Unit of Time

#### 8. Write fundamental units in F.P.S. system.

There are three fundamental quantity i.e. a. Length, b. Mass, c. Time. The F.P.S. unit of these quantities are given in the following –

• ft ⇒ Foot ⇒ Unit of Length
• lb ⇒ Pound ⇒ Unit of Mass
• s ⇒ Second ⇒ Unit of Time

#### 9. Write some fundamental units in S.I. system.

Scientists add some more fundamental units like temperature, electricity etc. for the purpose of uniformity. Also an universal system of unit is adopted to express them. That system is called S.I. system. S.I. means International System of Units and S.I. is abbreviated from the French Système international (d’unités). Followings are some S.I. units of some quantities  –

Quantity Unit Symbol
Length
Metre
m
Mass
Kilogram
kg
Time
Seconds
s
Current
Ampere
A
Temperature
Kelvin
Heat
Joule
J
Force
Newton
N
Power
Watt
W
Frequency
Hertz
Hz
Density
mass/volume

Kg/m3

#### 10. Write unit conversion table of mass. Also write some big units of mass.

Gram Table (Mass) ⇒

1 Kilogram = 103 Gram = 1000 Gram
1 Hectogram = 102 Gram = 100 Gram
01 Decagram = 101  Gram = 10 Gram
Gram
1 Decigram = (1/10) Gram = 10-1 Gram = 0.1 Gram
1 Centigram = (1/100) Gram = 10-2 Gram = 0.01 Gram
01 Milligram = (1/1000) Gram = 10-3 Gram= 0.001 Gram

• In addition, some big units of mass ⇒

1 Quintal = 100 Kg , 1 Metric Ton = 1000 Kg

#### 11. Write unit conversion table of length. Also write some big and small units of length.

Metre Table (Length) ⇒

1 Kilometre = 103 Metre = 1000 Metre
1 Hectometre = 102 Metre = 100 Metre
01 Decametre = 101  Metre = 10 Metre
Metre
1 Decimetre = (1/10) Metre = 10-1 Metre = 0.1 Metre
1 Centimetre = (1/100) Metre = 10-2 Metre = 0.01 Metre
01 Millimetre = (1/1000) Metre = 10-3 Metre= 0.001 Metre

• In addition some smaller units of length ⇒

1 Micron (µ) = 10-6 Metre
1 Angstrom (AO) =10-10 Metre
01 (X.U.) = 10-13 Metre

• Also very big unit of length ⇒

1 Light year =9.46×1015 Metre.

#### 12. Write unit conversion table of volume.

Litre Table (Volume) ⇒

1 Kilolitre = 103 Litre = 1000 Litre
1 Hectolitre = 102 Litre = 100 Litre
01 Decalitre = 101  Litre = 10 Litre
Litre
1 Decilitre = (1/10) Litre = 10-1 Litre = 0.1 Litre
1 Centilitre = (1/100) Litre = 10-2 Litre = 0.01 Litre
01 Millilitre = (1/1000) Litre = 10-3 Litre= 0.001 Litre

#### 13. Write unit conversion table of time.

Following is the conversion table of  Second (Time)

1 Year = 365 Days
1 Day = 24 Hours
60 Minutes = 1 Hour
1 Minute = 60 Second
1
Second = 1 / (24 x 60 x 60) Day ⇒ ( 1/86,400 ) Day
So, 86,400 seconds = 1 Day

#### 14. Write different conversion factors between foot and metre.

Followings are some conversion factors between foot and metre –

1 m = 100 cm = 3.2804 ft
1 ft = 30.48 cm = 0.3048 m
So, 1 ft2 = 0.0929 m2
1 ft3 = 0.0283 m3
1 m3 = 35.32 ft3
In addition,  1 mile = 1609 m = 1.609 km

##### Q15. Write some Greek letters that are used in science.

Followings are some common Greek letters that are used in science –

⇒ alpha, β ⇒ beta , γ ⇒ gamma
λ ⇒ lambda, θ ⇒ theta,  ν ⇒ nu
⇒ mu, ε ⇒ epsilon, Ψ ⇒ psi
⇒ phi,  Ω ⇒ capital omega,  ω ⇒ small omega,
σ ⇒ sigma,  π ⇒ pi, δ ⇒ delta

##### Mathematical Questions – Units –  Scalar Quantity Vector Quantity ⇒

a) Area of a garden is 1 m2. What will be it in cm2?
1 m2 =  1 m x 1 m = 100 cm x 100 cm = 10000 cm2 = 104 cm2.

b) Diameter of an iron sphere is 6 metre. Find its volume.
Volume of a sphere  = (4/3) πr3. Radius = Diameter/2 = 6/2 metre = 3 metre. So volume = (4/3) x 3.14 x 33 m3 = 113 m3.

c) An object weighs 175 g in air. It’s volume is 50 cm3. Calculate its density.
Density = Weight/Volume = (175/50) g/cm3 = 3.5 g/cm3.

d) Density of silver is 10.5 g/cm3. What it will be in S.I. unit?
1 g = 10 -3 kg. 1 cm = 10 -2 m. So 10.5 g/cm3 = 10.5 x [10 -3 kg/(10 -2m)3] = 10.5 x 10 -3 x 10 6 kg/m3 = 10.5 x 10 3 kg/m3.

e) Density of iron is 7.5 kg/m3. What will be volume of 10 kg iron piece?
Density = Weight/Volume. So Volume = Weight/Density =10/7.5 m3 = 1.33 m3.

f) One container is filled with kerosene. Weight of the kerosene is 8000 kg. Density of kerosene is 800 kg/m3. What will be internal volume of the container?
Density = Weight/Volume. So Volume = Weight/Density =8000/800 m3 = 10 m3.

g) One proton weighs 1.67×10 -27 kg. Then how many protons in 1 kg?
No. of protons = 1 kg / 1.67×10 -27 kg = 0.598 x10 26.

###### Multiple Choice Questions – Units –  Scalar Quantity Vector Quantity ⇒

i) Which quantity has no unit – a) density, b) relative density, c) heat, d) frequency?
b) relative density.
ii) Which is 1 micron (µ) – a) 10-8 cm, b)10-6 cm, c) 10-4 cm, d) 10-12 .
a) 10-8 cm.
iii) How many kilograms in 1 centigram – a) 10-2, b) 10-3, c) 10-4, d) 10-5?
d) 10-5.
iv) Which is the unit of  density – a) litre, b) m3, c) kg/m3, d) cm3?
c) kg/m3.

Scalar Quantity Vector Quantity – To Be Continued – Scalar Quantity Vector Quantity