Question

In: Physics

Show that the equation v2=v02 −2g(y−y0) is dimensionally consistent. (use dimensional analysis)

Show that the equation v2=v02 −2g(y−y0) is dimensionally consistent. (use dimensional analysis)

Solutions

Expert Solution

Given equation is:-

Where ,

  •    : is the final velocity measured in .
  • : is the initial velocity measured in .
  •     : is the acceleration due to gravity measured in
  •     : is the position (or distance) measured in (meters).

Above physical quantities can be expressed in terms of some basic dimensions given below in SI units,

  • : Length in meters ()
  • : Time in seconds ()

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,

  • : Velocity       =
  • : Velocity       =
  •    : Acceleration =
  •    : distance       =
  • : distance      =

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.


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