Question

The time dependence of a physical quantity $p$ is given by $p=p_0$ exp. $(-\alpha t^2)$, where $\alpha$ is a constant and $t$ is the time. The constant $\alpha$

• A. is dimensionless
• B. has dimensions $T^{-2}$
• C. has dimensions $T^2$
• D. has dimensions of $p$

Answer 1

The correct option is B has dimensions $T^{-2}$

Term inside the exponential in $p=p_{0}exp(-\alpha t^2)$ is dimensionless.
$\therefore \alpha =\frac{1}{t^2}=\frac{1}{T^2}=\left[T^{-2}\right]$