Question

A physical quantity $P$ is given by the relation, $P=P_0{e}^{(-\alpha t^2)}$. If $t$ denotes the time, the dimensions of constant $\alpha$ are

• A. $\left[T\right]$
• B. $\left[T^2\right]$
• C. $\left[T^{-1}\right]$
• D. $\left[T^{-2}\right]$

Answer 1

The correct option is D $\left[T^{-2}\right]$

Given,

$P=P_0{e}^{(-\alpha t^2)}$

As we know, both $P$ and $P_0$ are pressure, it have the same units. Therefore, $\alpha t^2$ must be dimensionless for which,

$\alpha =\frac{1}{T^2}=T^{-2}$

So the dimension of $\alpha$ is $\left[T^{-2}\right]$.