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 ?

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) A2 - B2 C2 (B) ((A - C)/D) (C) (A/B) - C (D) (C/BD) - (AD2/C)

Tardigrade Admin · Accepted Answer

AD = C ℓ n ( BD ) (B) (D) arrow dimensionless [ AD ]=[ C ] Checking options one by one (A-C/D)

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

$A^{2} - B^{2} C^{2}$

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

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

$\frac{C}{B D} - \frac{A D ^{2}}{C}$

$A D = C ℓ n (B D)$
$(B) (D) \to$ dimensionless
$[A D] = [C]$
Checking options one by one
$\frac{A - C}{D}$

Q. 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 ?

A2−B2C2

D(A−C)​

BA​−C

BDC​−CAD2​