Physics - Unit & Dimension Question with Solution | TestHub

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

So, its dimension is  $\left[\lambda \right]=\left[T^{-1}\right]$

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

$\left[\frac{dv}{dx}\right]=\frac{\left[L^1{T}^{-1}\right]}{\left[L^1\right]}=\left[T^{-1}\right]$