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Question: The time dependence of a physical quantity p is given by p = \(p_{0}e^{- \alpha t^{2}}\), where a is...

The time dependence of a physical quantity p is given by p = p0e−αt2p_{0}e^{- \alpha t^{2}}, where a is constant and t is time. The constant a -

A

(a) Is dimensionless

A

(b) Has dimensions T-2\text{T}^{\text{-2}}

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(c) Has dimensions T2

A

(d) Has dimensions of p

Explanation

Solution

(b)

Sol. Powers are always dimensionless

\ [at2] = [M0 L0 T0]\lbrack at^{2}\rbrack\ = \ \lbrack Μ^{0}\ L^{0}\ Τ^{0}\rbrack

or [α] = [M0 L0 T −2]\lbrack\alpha\rbrack\ = \ \lbrack Μ^{0}\ L^{0}\ Τ\ ^{- 2}\rbrack