RRB Technician Grade I 19 Dec 2024 Shift 2 Paper

Concept:Dimensional consistency of an equation implies that every term in the equation follows the principle of homogeneity of dimensions.Explanation:According to the principle of homogeneity, all terms on both sides of a physical equation must have the same dimensional formula.For example, in $KE = \frac{1}{2}mv^2$, the dimensions of kinetic energy are $[M][L]^2[T]^{-2}$ and the dimensions of $\frac{1}{2}mv^2$ are also $[M][L]^2[T]^{-2}$.This shows that the equation is dimensionally consistent.Dimensional consistency is necessary for an equation to be physically valid, but it does not guarantee that the equation is correct in all circumstances.It also does not directly mean that units can be easily converted or that the physical quantities are related correctly.Therefore, dimensional consistency specifically implies that the equation respects the principles of homogeneity of dimensions.Answer:Option B: The equation respects the principles of homogeneity of dimensions.