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Question

A physical quantity $$P$$ is given by the relation, $$P={P}_{0}{e}^{(-\alpha {t}^{2})}$$. If $$t$$ denotes the time, the dimensions of constant $$\alpha$$ are


A
[T]
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B
[T2]
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C
[T1]
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D
[T2]
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Solution

The correct option is D $$[{T}^{-2}]$$
Given,

$$P=P_0e^{(-\alpha t^2)}$$

As we know, both $$P$$ and $$P_0$$ are pressure, it have the same units. Therefore, $$\alpha t^2$$ must be dimensionless for which,

$$\alpha=\dfrac{1}{T^2}=T^{-2}$$

So the dimension of $$\alpha$$ is $$[T^{-2}]$$.

Physics

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