If A and B are two physical quantities having different dimensions then which of following can't

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1.Units, Dimensions and Measurement

medium

If $A$ and $B$ are two physical quantities having different dimensions then which of the following can't denote a physical quantity?

A

$A + \frac{{{A^3}}}{B}$

B

$\exp \,\left( { - \frac{A}{B}} \right)$

C

$AB^2$

D

$\frac{A}{{{B^4}}}$

Solution

For $(1)$$: \mathrm{A}$ and $\frac{\mathrm{A}^{3}}{\mathrm{B}}$ may have same dimension.

For $( 2):$ As $A$ and $B$ have different dimen-

sion so $\exp \left(-\frac{\mathrm{A}}{\mathrm{B}}\right)$ is meaningless.

For $(3)$ $: \mathrm{AB}^{2}$ is meaningful.

For $4)$ $: \mathrm{AB}^{-4}$ is meaningful.

Standard 11

Physics

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(JEE MAIN-2019)