Q 11-01-019JEE MainEAMCET 1986 (Engineering)Medium
Dimensional analysis of the equation
$$(\text{Velocity})^x = (\text{Pressure difference})^{3/2}\,(\text{Density})^{-3/2}$$
gives the value of $x$ as
Answer: (C) $3$
Combine the right-hand side first: $\dfrac{\text{Pressure}}{\text{Density}} = \dfrac{[ML^{-1}T^{-2}]}{[ML^{-3}]} = [L^2T^{-2}]$
So the right-hand side is $\left(\dfrac{P}{\rho}\right)^{3/2} = [L^2T^{-2}]^{3/2} = [L^3T^{-3}] = [LT^{-1}]^3$
That is (velocity)$^3$, so $x = 3$.
Solution by Sreeraj P, M.Sc Physics