Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
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 $\alpha$
PhysicsUnits and DimensionsVITEEEVITEEE 2013
Options:
  • A is a dimensionless
  • B has dimensions of $P$
  • C has dimensions of $T^{-2}$
  • D has dimensions of $T^{2}$
Solution:
2145 Upvotes Verified Answer
The correct answer is: has dimensions of $T^{-2}$
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
$\alpha=\frac{1}{T^{2}}=T^{-2}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.