Determine if the following equation is dimensionally correct: h = 2 S r g 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: [h] = [L] Dimensions of the quantities on the right-hand side: [S] = [M T⁻²] [ ] = [M^0 L^0 T^0] [ ] = [M L⁻³] [r] = [L] [g] = [L T⁻²] Substituting these dimensions into the right-hand side: RHS = [M T⁻²] [M L⁻³] [L] [L T⁻²] RHS = [M T⁻²] [M L⁻¹ T⁻²] RHS = [L] Since the dimensions of the left-hand side equal the dimensions of the right-hand side, the equation is dimensionally correct.