Question

p=(pgh)^1/2 is dimensionally correct​

Answer 1

Answer: No

Explanation:

We know the pressure p = force/area

so dimension of p = MLT⁻² / L² = M L⁻¹ T⁻²

now we will find the dimension of $\sqrt{\rho g h}$

Dimension of ρ = M L⁻³

Dimension of  g = L T⁻²

Dimension of h = L

So the dimension of ρgh = M L⁻³  L T⁻²  L = M L⁻¹ T⁻²

So the dimension of $\sqrt{\rho g h} = \sqrt{M L^{-1} T^{-2}}$

Hence, $p = \sqrt{\rho g h}$ is not dimensionally correct.

Actual expression is $p = \rho g h$ , which is dimensionally correct​.