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  4. The time dependence of a physical quantity p is given by p=p0e-at2, where α is constant and t is time. The constant α

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Q. The time dependence of a physical quantity $p$ is given by $p=p_0e^{-at^2}$, where $\alpha$ is constant and $t$ is time. The constant $\alpha$

Physical World, Units and Measurements

Solution:

Given : $p = p_{0}e ^{-\alpha t^2}$
$\alpha t^{2}$ is dimensionless
$\therefore \left[\alpha \right] = \frac{1}{\left[t^{2}\right]} = \frac{1}{\left[T^{2}\right]} = \left[T^{-2}\right]$