Identify the pair of physical quantities that have same dimensions:

Question

Aicharya · Accepted Answer

Decay constant is measured per unit time, $λ = s^{- 1}$

So, its dimension is $[λ] = [T^{- 1}]$

We know velocity gradient is defined as rate of change in velocity per unit of distance. So, dimension of velocity gradient is

$[\frac{d v}{d x}] = \frac{[L^{1} T^{- 1}]}{[L^{1}]} = [T^{- 1}]$

Solution