Let us consider an equation $\frac{1}{2} m u^{2} = m g h$ , where $m$ is mass of the body, $v$ its velocity, $g$ is the acceleration due to gravity and $R$ is the Right. Check whether this equation is dimensionally correct.

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Solution

In order to compare the dimensions, the constant terms are ignored.
$m u^{2} = m g h$

Substitute the units for both the quantities:
$\Rightarrow k g (m s^{- 1})^{2} = k g m s^{- 2} m$

Compare the dimensions:
$\Rightarrow [M L^{2} T^{- 2}] = [M L^{2} T^{- 2}]$

The equation is dimensionally correct.

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