Physics - Unit & Dimension Question with Solution | TestHub

The given equation is $p=p_0{e}^{\left(-\alpha t^2\right)}$. For the exponent of $e$ to be dimensionless, the product $\alpha t^2$ must be dimensionless. Since $t$ is time, its dimension is $[T]$. Therefore, the dimension of $\alpha t^2$ is $[\alpha ][T{]}^2$. For this to be dimensionless, $[\alpha ][T{]}^2=[M^0{L}^0{T}^0]$. Thus, $[\alpha ]=[T^{-2}]$.

The final answer is $\boxed{B}$