Physical World Units and Measurements - Result Question 26

28. The time dependence of a physical quantity $p$ is given by $p=p_0 \exp (-\alpha t^{2})$, where $\alpha$ is a constant and $t$ is the time. The constant $\alpha$

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(a) is dimensionless

(b) has dimensions $T^{-2}$

(c) has dimensions $T^{2}$

(d) has dimensions of $p$

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Answer:

Correct Answer: 28. (b)

Solution:

  1. (b) In $p=p_0 \exp (-\alpha t^{2})$, where $\alpha t^{2}$ where is dimensionless

$\therefore \alpha=\frac{1}{t^{2}}=\frac{1}{[T^{2}]}=[T^{-2}]$