Using dimensional analysis for the given equation,
T=KS23ρr3
⇒[K]=[ρ21][r23][T][S43]⇒[K]=[M21L−23][L23][T][M43T−23]⇒[K]=[M41T−21]
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 = Dimensions of R.H.S
∴ Option (D) is correct.