homogeneity of an equation
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Dimensional AnalysisTo 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 the body after a time t is given by the equation
s = ut + 1/2 at2
Show that the equation is dimensionally homogeneous.
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
= LAll the terms have the same dimension = 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
= LAll the terms have the same dimension = LTherefore the equation is dimensionally homogenious.
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