Question

The time dependence of a physical quantity $P$ is given by $P=P_{0} e \alpha P\left(-\alpha t^{2}\right)$ where $\alpha $ is a constant and $t$ is time. The constant $\alpha $

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

Answer 1

Answer: (C)

Given, $P=P_{0} \exp \left(-\alpha t^{2}\right)$
As $P$ and $P_{0}$ have the same units,
therefore $\alpha t^{2}$ must be dimensionless for which
$\alpha=\frac{1}{T^{2}}=T^{-2}$