Determine if the following equation is dimensionally correct: = 1 2 mgl I where h = height, S = surface tension, = density, P = pressure, V = volume, = coefficient of viscosity, = frequency and I = moment of inertia.

Step-by-step solution

Dimensions of the left hand side (LHS): [ ] = [T⁻¹] Dimensions of the terms on the right hand side (RHS): [m] = [M] [g] = [L T⁻²] [l] = [L] [I] = [M L^2] Substituting these into the expression under the square root: [ mgl I ] = [M][L T⁻²][L] [M L^2] = [T⁻²] Taking the square root for the RHS: [ mgl I ] = [T⁻²] = [T⁻¹] Since the dimensions of the LHS and RHS are equal, the equation is dimensionally correct.