Question

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

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

Answer 1

Answer: (B)

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

Answer 2

$AD = C \ell n ( BD )$
$(B) (D) \rightarrow$ dimensionless
$[ AD ]=[ C ]$
Checking options one by one
$\frac{A-C}{D}$