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)

has dimensions of $T^{-2}$

Answer 2

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