Rule out or accept the following formulae for kinetic energy on t… - Vidyadip

Question

Rule out or accept the following formulae for kinetic energy on the basis of dimensional arguments.

$\text{K}=\frac{3}{16}\text{mv}^2$
$\text{K}=\frac{1}{2}\text{mv}^2+\text{ma}$
$\text{K}=\frac{1}{2}\text{mv}^2$

✓

Answer

Dimension of $\text{L.H.S.}$ and $\text{R.H.S.}$ are same in $(i)$ and $(iii).$ So they are accepted.

$\text{K}=\frac{1}{2}\text{mv}^2+\text{ma}$ and $\Big[\frac{1}{2}\text{mv}^2\Big]\neq[\text{ma}].$

So it is wrong.

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