DIMENSIONS
Dimensions
It is
discusses three fundamental dimensions in physics. All other dimensions are
formed by using these three fundamental dimensions. Basic dimensions –
[Length]
– L
[Mass]
– M
[Time]
– T
(But it is having other additional dimensions also, Temperature –θ
, Electric current – I, Intensity of light – L, number of moles
– n)
If a physical quantity is given in square brackets, it represents a dimension of the
quantity.
No dimensions
for the quantities of units less.
Examples:
Index of refraction,
strain, coefficient of friction, velocity ratio, efficiency, relative humidity,
relative density
Note:
however the plane angle and solid angle has units, they do not have
dimensions.
The
dimensions derived by using basic dimensions are called derived dimensions.
Example 1:
Dimension of
velocity
Example 2: Dimension of momentum
Example 3: Dimension of heat capacity.
Example 4: Electric charge
Uses of Dimensions
1. Test the accuracy of a formula
The
relation among few physical quantities given in mathematical form by a formula.
In a correct equation, the dimensions of the physical quantities on the sides
of the equal sign should be equal to each other.
The
relation among the three quantities of A, B, and C is when,
[Length]
– L
[Mass]
– M
[Time]
– T
When some quantities are related as addition or subtraction, those adding or subtracting quantities should have equal dimensions.
When
the relation among quantities is
When
the relation is,
Further
here, 
The
relations among dimensions also have for the units.
Example:
Show
that the following equations are dimensionally correct. 
2. To find the dimension or units of a
physical quantity or a constant
In
a correct formula, the dimensions of the quantities of the two sides of equal
sign is equal. Added or subtracted quantities of a formula has equal units. By
using this matter we can find the dimensions or units of a quantity.
Example: If 
are Pressure, Volume,
number of moles and absolute temperature. Find the SI units of
.
Example:
The rate of
flowing heat through a uniform cross sectional metal rod,
What is the dimensions
of conductivity (k)?
3. Building up a relationship among few
quantities
By
analyzing dimensions among quantities, relations can be built up to maximum of
4 quantities. We cannot take the values of constants by this method.
Example:
It is assumed that the periodic
time (T) of a simple pendulum is depend on the following quantities.
i.
Length
of the pendulum(
)
ii.
Acceleration
due to gravity (g)
iii.
Mass
of the bob (m)
If the constant of
proportionality is determined as
, build a relation among these quantities.
Example:
The volume flow rate of
a fluid through a horizontal hair tube turbulently in steady flow is depend on
the following quantities.
i.
Radius
of the tube(r)
ii.
Pressure
gradient of the tube(
)
iii.
Coefficient
of viscosity of the fluid (
)
Past Papers
2000 Paper I
Problem 02
2002 Paper I
Problem 01
2004 Paper I
Problem 01
2005 Paper I
Problem 01
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