PHYSICS CLASS: Unit And Dimension
QUANTITIES AND UNIT
The term has to do
with measurement. It is the property of things that can be measured in
measurement, the question being asked is how much, how big, how long, how fast
etc. The two types of quantities are
Fundamental quantities
Derived quantities
Fundamental quantities are the basic
quantities upon which other quantities are built. The units of the basic
quantities are called fundamental units.
FUNDAMENTAL
QUANTITIES

SYMBOL

FUNDAMENTAL UNIT

Mass

M

Kilogram Kg

Length

L

Meter M

Time

t

Seconds S

Angle

á¶¿

Radian Rad

Amount of substance

N

Mole
Mol

Temperature

T

Kelvin K

Electric Current

I

Ampere A

Luminous Intensity


Candela Cd

(B) DERIVED
QUANTITIES
They are quantities which can be derived from the
fundamental quantities. They include quantities such as; Area, volume,
velocity, acceleration, momentum etc. The units of these derived quantities are
called derived units.
EXAMPLES
Area = length
(m) x length (m) = Meter squared = M^{2}
Velocity = distance (m) = meter per
seconds = MS^{1}
^{ }Time (s)
Accelerator = Velocity (MS^{1})
= MS^{11 }= MS^{2}
Time (S)
DIMENSION
The dimensions of physical quantities tell us how those
quantities relate to the fundamental quantities. The three fundamental
quantities in mechanics and their dimensions and unit are
Quantity

Dimensions

Unit

Mass

M

Kg

Length

L

M

Time

T

S

Below is the dimension of some physical quantities.
S/No

Quantity

Unit

Dimensions

1

Velocity

MS^{1}

LT^{1}

2

Acceleration

MS^{2}

LT^{2}

3

Force

Kgm^{2}

MLT^{2}

4

Momentum

KgmS^{1}

MLT^{1}

5

Area

M^{2}

L^{2}

6

Volume

M^{3}

L^{3}

7

Density

Kgm^{3}

ML^{3}

8

Pressure

Kgm^{1}S^{2}

ML^{1}T^{2}

9

Energy

Kgm^{2}S^{2}

ML^{2}T^{2}

10

Power

KgM^{2}S^{3}

ML^{2}T^{3}

11

Surface tension

KgS^{2}

MT^{2}

12

Young modulus

Kgm^{1}S^{2}

ML^{1}S^{2}

13

Impulse

KgmS^{1}

MLS^{1}

14

moment

Kgm^{2}S^{2}

ML^{2}S^{2}

SIMPLIFIED 1: If
the formula for the period of Acceleration of a simple pendulum bulb is T = L^{x}
g^{y} find the value of x and y
Solution:
L^{x} g^{y}
And L are already in dimension but g =
Acceleration due to gravity thus SI unit is the SI unit of acceleration
=MS^{} ^{2} = LT^{2}
= L^{x} (LT^{2})^{y}
= L^{x} L^{y}T^{2y}
= L^{x+y
}T^{2y}
() 1 =
2Y
Y=  1/2
(L) = 0 = x +y
But y =  1/2
O = x + (1/2)
O = x – 1/2
1/2 = x
Y = 1/2, x = 1/2
SIMPLIFIED 2: at
what respective values of x, y and z would the unit of force be dimensionally
equivalent to M^{X}L^{Y}T^{Z}
Solution
The dimension of force is
MLT ^{2}
MLT^{2} = M^{x}L^{y}T^{z}
M^{x}L^{y}T^{z} = M^{1}
L^{1} T^{2}
X = 1, y = 1, z = 2
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