Question

Check the correctness of the equation $F_C=\frac{m{v}^2}{r}$, where the terms have their.

Answer 1

Dimensional formula of force $=m\times a$

$mxa=\frac{mxv}{t}$

$L.H.S=F=M^1{L}^1{T}^{-2}---------\left(1\right)$

$R.H.S=\frac{m{v}^2}{r}$
$=\frac{M^1(L^1{T}^{-1}{)}^2}{L}$

$=\frac{M^1{L}^2{T}^{-2}}{L}$

$=M^1{L}^1{T}^{-2}-----------\left(2\right)$

By equation 1 and 2
$L.H.S=R.H.S$
Since the dimensions of $F$ and $\frac{m{V}^2}{r}$ are equal... so equation is dimensionally correct