Given below are two statements: One is labelled as Assertion (A)...

Using dimensional analysis for the given equation,

$T = K\sqrt{\dfrac{ρ{r}^{3}}{{S}^{\dfrac{3}{2}}}}$

$⇒ \left[K\right] = \dfrac{\left[T\right]\left[{S}^{\dfrac{3}{4}}\right]}{\left[{ρ}^{\dfrac{1}{2}}\right]\left[{r}^{\dfrac{3}{2}}\right]} ⇒ \left[K\right] = \dfrac{\left[T\right]\left[{M}^{\dfrac{3}{4}}{T}^{- \dfrac{3}{2}}\right]}{\left[{M}^{\dfrac{1}{2}}{L}^{- \dfrac{3}{2}}\right]\left[{L}^{\dfrac{3}{2}}\right]} ⇒ \left[K\right] = \left[M\dfrac{1}{4}{T}^{- \dfrac{1}{2}}\right]$

Therefore, $K$ is not dimensionless. Hence, Assertion is false.

For dimensional validity of the given equation, $K$ can not be dimensionless. If it is dimensionless then

Dimensions of L.H.S $\ne$ Dimensions of R.H.S

$∴$ Option (D) is correct.