Question

A, B, C and D are four different physical quantifies having different dimensions. None of them is dimensionless. But we know that the equation $AD=Cln\left(BD\right)$ holds true. Then which of the combination is not a meaningful quantity

• A. $\frac{C}{BD}-\frac{A{D}^2}{C}$
• B. $A^2-B^2{C}^2$
• C. $\frac{A}{B}-C$
• D. $\frac{(A-C)}{D}$

Answer 1

The correct option is D $\frac{(A-C)}{D}$

Since the product $BD$ is inside logarithmic function, it must be dimensionless. Hence $\left[B\right]\left[D\right]=1$.

Also, from equality of two quantities in the expression, $\left[C\right]=\left[A\right]\left[D\right]$. This expression clearly means that dimensions of $A$ and $C$ are not same since $D$ is not dimensionless. Hence $A$ and $C$ cannot be subtracted and hence option D is not a meaningful quantity.