Question

Identify the pair of physical quantities that have same dimensions :

Answer 1

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

$\Rightarrow$ Dimensions are $\frac{\left[L{T}^{-1}\right]}{\left[L\right]}=\left[T^{-1}\right]$

Decay constant $\lambda$:

$-\frac{1}{N}\frac{dN}{dt}=\lambda$

So, the dimension of $\lambda$ will be $\left[T^{-1}\right]$.

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

Hence, $\left(A\right)$ is the correct answer.