# Question #4aee3

Jan 1, 2017

Given is an equation

$a = {v}_{\text{average}}^{2} / R$

LHS of the equation is acceleration $a$.
Units of acceleration are $m {s}^{-} 2$
$\therefore$ Units of LHS of the equation are $m {s}^{-} 2$
Dimensions of LHS are ${\text{M"^0"L"^1"T}}^{-} 2$

RHS of the equation is ${v}_{\text{average}}^{2} / R$
Units of velocity ${v}_{\text{average}}$ are $m {s}^{-} 1$
In the denominator we have distance $R$, units are $m$
$\therefore$ Units of RHS of the equation are ${\left(m {s}^{-} 1\right)}^{2} / m$
$\implies$ Units of RHS of the equation are $m {s}^{-} 2$

We see that units as well dimensions of LHS are same as of RHS.

Proved