In: Physics
Show that the equation v2=v02 −2g(y−y0) is dimensionally consistent. (use dimensional analysis)
Given equation is:-
Where ,
Above physical quantities can be expressed in terms of some basic dimensions given below in SI units,
Equation is,
The equation contains three terms as, V2, V02 and 2g (y - y0) . In order to have consistency, all the three terms must have same dimensions.
Taking the equation in terms of dimensions as,
Therefore equation becomes,
As we can see, all the terms have unit of velocity square and have same dimensions. Thus the equation is dimensionally consistent.