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1.Units, Dimensions and Measurement
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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
Similar Questions
Match the following two coloumns
Column $-I$ | Column $-II$ |
$(A)$ Electrical resistance | $(p)$ $M{L^3}{T^{ – 3}}{A^{ – 2}}$ |
$(B)$ Electrical potential | $(q)$ $M{L^2}{T^{ – 3}}{A^{ – 2}}$ |
$(C)$ Specific resistance | $(r)$ $M{L^2}{T^{ – 3}}{A^{ – 1}}$ |
$(D)$ Specific conductance | $(s)$ None of these |
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