Dimensional Analysis
To check Homogeneity of an equation
Example 1
• For a body in linear motion under uniform
acceleration a, if u is its initial velocity, the
displacement s of ...
Solution:
s = ut + 1/2 at2
Left hand side
[s] = L
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
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...
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...
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Homogeneity of an equation

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Example on how to check the homogeneity of an equation

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Homogeneity of an equation

  1. 1. Dimensional Analysis To check Homogeneity of an equation
  2. 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. 3. Solution: s = ut + 1/2 at2 Left hand side [s] = L
  4. 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. 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. 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.

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