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Question: The time dependence of a physical quantity P is found to be of the form P = \(P_{0}e^{- \alpha t^{2}...

The time dependence of a physical quantity P is found to be of the form P = P0e−αt2P_{0}e^{- \alpha t^{2}}where t is time and a is some constant. Then the constant a will –

A

Be dimensionless

B

Have dimensions of T-2T^{\text{-2}}

C

Have dimension of P

D

Have dimensions of P multiplied by

Answer

Have dimensions of T-2T^{\text{-2}}

Explanation

Solution

[at2] = 1 ⇒ [α] = T−2\lbrack at2\rbrack\ = \ 1\ \Rightarrow \ \lbrack\alpha\rbrack\ = \ Τ^{- 2}