JEE MAIN - Physics (2022 - 24th June Evening Shift - No. 1)

Identify the pair of physical quantities that have same dimensions:

velocity gradient and decay constant

Wien's constant and Stefan constant

angular frequency and angular momentum

wave number and Avogadro number

Velocity gradient $$ = {{dv} \over {dx}}$$

$$\Rightarrow$$ Dimensions are $${{[L{T^{ - 1}}]} \over {[L]}} = [{T^{ - 1}}]$$

Decay constant $$\lambda$$ has dimensions of $$[{T^{ - 1}}]$$ because of the relation $${{dN} \over {dt}} = - \lambda $$ N

$$\Rightarrow$$ Velocity gradient and decay constant have same dimensions.