Question

The time dependence of a physical quantily P is given by P =P(0) exp (-at×t) where a is constant and t is time. The constant a =?





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Answer 1

Given,

$P = P(0) {e}^{ - \alpha {t}^{2} }$

As we know both P and P(0) are pressure so it have the same units, therefore

$\alpha {t}^{2}$

must be dimensionless for which

$\alpha = 1 \div {t}^{2}$

So the dimension of α is [T^(−2)].