Example on how to check the homogeneity of an equation

1. Dimensional Analysis
To check Homogeneity of an equation

2. Example 1
• For a body in linear motion under uniform
acceleration a, if u is its initial velocity, the
displacement s of the body after a time t is given
by the equation
s = ut + 1/2 at2
Show that the equation is dimensionally
homogeneous.

3. Solution:
s = ut + 1/2 at2
Left hand side
[s] = L

4. Solution:
s = ut + 1/2 at2
Left hand side Right hand side
[s] = L i) [ut] = LT-1. T
= L
ii) [ 1/2 at2 ] = LT-2. T2
= L

5. Solution:
s = ut + 1/2 at2
Left hand side Right hand side
[s] = L i) [ut] = LT-1. T
= L
ii) [ 1/2 at2 ] = LT-2. T2
= L
All the terms have the same dimension = L

6. Solution:
s = ut + 1/2 at2
Left hand side Right hand side
[s] = L i) [ut] = LT-1. T
= L
ii) [ 1/2 at2 ] = LT-2. T2
= L
All the terms have the same dimension = L
Therefore the equation is dimensionally homogenious.