Units for constants in Column-$I$ and $SI$ unit is given in Column-$II$. Match the followings:
Column-$I$ Column-$II$
$(a)$ Wien's constant $(i)$ $W m^{-2} K^{-4}$
$(b)$ Stefan-Boltzmann's constant $(ii)$ $W m^{-1} K^{4}$
$(iii)$ $m K$

  • A
    $(a-i), (b-ii)$
  • B
    $(a-i), (b-iii)$
  • C
    $(a-ii), (b-i)$
  • D
    $(a-iii), (b-i)$

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Which of the following pairs of quantities do not have the same dimensions?

Estimate the average mass density of a sodium atom assuming its size to be about $2.5 \; \mathring{A}$. (Use the known values of Avogadro's number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase: $970 \; kg \; m^{-3}$. Are the two densities of the same order of magnitude? If so,why?

Names of units of some physical quantities are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the correct pairs in the lists:
$A$. $Pa \cdot s$$(i)$. $[L^2 T^{-2} K^{-1}]$
$B$. $N \cdot m \cdot K^{-1}$$(ii)$. $[MLT^{-3} K^{-1}]$
$C$. $J \cdot kg^{-1} \cdot K^{-1}$$(iii)$. $[ML^{-1} T^{-1}]$
$D$. $W \cdot m^{-1} \cdot K^{-1}$$(iv)$. $[ML^2 T^{-2} K^{-1}]$

Which of the following pairs of physical quantities does not have the same dimensional formula?

Select the pair from the following that does not have the same dimensions.

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