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.