A, B, C and D are four different physical qua | vedclass

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(D) In the equation $AD = C \ln(BD)$,the argument of the logarithmic function must be dimensionless. Therefore,the dimension of $BD$ must be $1$ (dime

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$\frac{A - C}{D}$

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(D) In the equation $AD = C \ln(BD)$,the argument of the logarithmic function must be dimensionless. Therefore,the dimension of $BD$ must be $1$ (dimensionless),i.e.,$[BD] = [M^0 L^0 T^0]$.This implies $[B] = [D]^{-1}$.Substituting this into the equation,we have $[AD] = [C] 	imes [1]$,so $[A][D] = [C]$.For a physical quantity to be meaningful in addition or subtraction,the dimensions of the terms must be identical.Checking option $D$: $\frac{A - C}{D}$. Here,$A$ and $C$ are being subtracted. Since $[A] = [C][D]^{-1}$ and $[C] = [A][D]$,the dimensions of $A$ and $C$ are different. Thus,$A - C$ is not a meaningful operation.

$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. We know that the equation $AD = C \ln(BD)$ holds true. Which of the following combinations is not a meaningful quantity?

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