Q91 / 120 · VITEEE 2013 · Physics
The time dependence of a physical quantity $P$ is given by $P=P_{0} e_{\alpha}\left(-\alpha t^{2}\right)$, where $\alpha$ is a constant and $t$ is time. The constant $\alpha$
- Ais a dimensionless
- Bhas dimensions of $P$
- Correct answerChas dimensions of $T^{-2}$
- Dhas dimensions of $T^{2}$
Solution
Given, $\mathrm{P}=\mathrm{P}_{0} \exp \left(-\alpha \mathrm{t}^{2}\right)$
As $\mathrm{P}$ and $\mathrm{P}_{0}$ have the same units, therefore $\alpha t^{2}$ must be dimensionless for which
$\alpha=\frac{1}{T^{2}}=T^{-2}$
Hence, the correct answer is option: 'C'.