Question

Check the correctness of equqtion PE=Mgh dimensionally

Answer 1

Here. . . . . . . . . .

Answer 2

Explanation:

Here we are given the expressions of kinetic energy and potential energy.

The expression for P.E is given as, P.E=mgh.

Let us first find The dimensional formula for $1/2mv^2$ can be written as,

The mass,  $m=[M]$

The formula for velocity $v=d/t$

where d stands for displacement and t stands for time.

The dimensional formula for velocity will be

$v=d/t=L/T=LT^{-1}$

Therefore,

$v^2=L^2T^{-2}$

The dimensional formula for  can be written as, $1/2mv^2=[ML^2T^{-2}]$

And, the dimensional formula for potential energy for $mgh$

The mass, $m=[M]$

Acceleration can be written as, $a=d/t^2$

where d stands for the distance and t stands for the time.

The dimensional formula for acceleration can be written as, $a=L/T^2=LT^{-2}$

The dimensional formula for the acceleration due to gravity is, therefore,

$g=[LT^{-2}]$

The dimensional formula for height $h=[L]$

The dimensional formula for $mgh$can be written as, $mgh=[ML^2T^{-2}]$

The dimensions of both $1/2mv^2$and $mgh$are the same.

Therefore we can say that the relation $mgh=1/2mv^2$ is dimensionally correct.