Page 124 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

EXERCISE 10 : Units & Dimensions

The Dimension of a physical quantity refers to the way it can be expressed in terms of fundamental units.
These fundamental units are the basic units that all other units are drived from it.There are seven internationally
recognized fundamental units, which are.
Meter (m) for Length
Kilogram (kg) for mass
Second (s) for time

Ampere (A) for electric current
Kelvin (K) for temperature
Candela (cd) for luminous intensity
Mol (mol) for amount of substance
The dimension of a physical quantity is written using exponents in square brackets, where each exponent represent
the power to which corresponding fundamental unit is raised. For example dimension of length is denoted by
M°L T°, where M represents mass, L represents length, and T represents lime. In this case, the exponent 1 for
1
length (L) signifies that length is raised to the power of 1 and the exponent of O for mass (M) and time (T) indicate
that they are not involved in the fundamental unit of length.

Some additional example of dimensions of physical quantities which are called derived physical quantities, means
these are derived from one or more fundamental physical quantities.
Area (M°L²T°)
Volume (M°L T°)
3
Speed (M°L T )
-1
1
Acceleration (M°L T )
-2
1
Force (M L T )
1 1
-2
Energy (M L T )
-2
2
Application
Dimensional formulas have many applications, some of them are mentioned below
Verify the correctness of equations
Coverting quantities between units
Expressing quantities in fundamental units

Problem 1
Find the dimensional formula of momentum
Solution
Momentum = mass x velocity

we know,
Dimensional formula for mass M
Dimensional formula for Velocity = LT -1
Hence Dimensional formula for Momentum = m x v
(P) = MLT -1

111