The pressure P of a fluid is given by the relation P = - x^2 t , where x represents distance, t represents time, and , are dimensional constants. The dimensional formula of the ratio is equivalent to that of :

Step-by-step solution

According to the principle of homogeneity of dimensions, the terms added or subtracted must have the same dimensions. Therefore, [ ] = [x^2] = L ^2 From the given equation, the dimension of is: [ ] = [ ] [P][t] Substituting the dimensions of pressure [P] = ML ⁻¹ T ⁻² and time [t] = T : [ ] = L ^2 ( ML ⁻¹ T ⁻²)( T ) = L ^2 ML ⁻¹ T ⁻¹ = M ⁻¹ L ^3 T Now, the dimensional formula of the ratio is: [ ] = L ^2 M ⁻¹ L ^3 T = ML ⁻¹ T ⁻¹ This is the dimensional formula for the coefficient of viscosity. Answer: Coefficient of