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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.

genius_generous answered 3 months ago

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