Two constants A and B have the dimensions of surface tension and coefficient of viscosity, respectively. If v denotes velocity, x denotes distance, and t denotes time, which of the following equations is dimensionally consistent?

Step-by-step solution

The dimensional formula for surface tension A is [A] = [MT⁻²] . The dimensional formula for coefficient of viscosity B is [B] = [ML⁻¹T⁻¹] . Let us evaluate the dimensions of the ratio A B : [ A B ] = [MT⁻²] [ML⁻¹T⁻¹] = [LT⁻¹] This matches the dimensions of velocity v . Therefore, the prefactor in the equation must be A B . For an equation to be dimensionally consistent, the argument of the logarithm must be dimensionless. Let us check the argument A t B x : [ A t B x ] = [ A B ] [t] [x] = [LT⁻¹] [T] [L] = [M^0L^0T^