Q 11-01-151JEE MainJEE Main 2022 (24 Jun, Shift 2)Easy
Identify the pair of physical quantities that have same dimensions:
Answer: (A) Velocity gradient and decay constant
Velocity gradient $\dfrac{dv}{dx}$ has dimensions $[\text{L}\text{T}^{-1}]/[\text{L}] = [\text{T}^{-1}]$. The decay constant $\lambda$ (from $N = N_0e^{-\lambda t}$) also has dimensions $[\text{T}^{-1}]$.
The other pairs differ: angular frequency is $[\text{T}^{-1}]$ but angular momentum is $[\text{M}\text{L}^2\text{T}^{-1}]$; wave number is $[\text{L}^{-1}]$ while Avogadro number is per mole; Wien's constant is $[\text{L}\,\text{K}]$ while Stefan's constant is $[\text{M}\text{T}^{-3}\text{K}^{-4}]$.
Solution by Sreeraj P, M.Sc Physics