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{\left ( A-C \right )}{D}

C.

\frac{A}{B}-C

D.

\frac{C}{BD}-\frac{(AD)^2}{C}

Answers (1)

A.D= C \ln \left ( B.D \right )

Hence \left [ B.D \right ]= are \: dimensionless

\left [ B \right ]= \left [ \frac{1}{D} \right ]...............(1)

&   \left [ A.D \right ]= \left [ C \right ]...............(2)

By using above two equation.

A- B2Cis correct.

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