The time dependence of a physical quantity P is given by P=P0 e α P(-α t2) where α is a constant and t is time. The constant α

Question

The time dependence of a physical quantity P is given by P=P0 e α P(-α t2) where α is a constant and t is time. The constant α  (A) is a dimensionless (B) has dimensions of P (C) has dimensions of T-2 (D) has dimensions of T2

Tardigrade Admin · Accepted Answer

Given, P=P0 exp (-α t2) As P and P0 have the same units, therefore α t2 must be dimensionless for which α=(1/T2)=T-2

Q. The time dependence of a physical quantity $P$ is given by $P = P_{0} e α P (- α t^{2})$ where $α$ is a constant and $t$ is time. The constant $α$

is a dimensionless

has dimensions of $P$

has dimensions of $T^{- 2}$

has dimensions of $T^{2}$

Given, $P = P_{0} exp (- α t^{2})$
As $P$ and $P_{0}$ have the same units,
therefore $α t^{2}$ must be dimensionless for which
$α = \frac{1}{T ^{2}} = T^{- 2}$

Q. The time dependence of a physical quantity P is given by P=P0​eαP(−αt2) where α is a constant and t is time. The constant α

is a dimensionless

has dimensions of P

has dimensions of T−2

has dimensions of T2

Given, P=P0​exp(−αt2) As P and P0​ have the same units, therefore αt2 must be dimensionless for which α=T21​=T−2

Q. The time dependence of a physical quantity $P$ is given by $P = P_{0} e α P (- α t^{2})$ where $α$ is a constant and $t$ is time. The constant $α$

has dimensions of $P$

has dimensions of $T^{- 2}$

has dimensions of $T^{2}$

Given, $P = P_{0} exp (- α t^{2})$
As $P$ and $P_{0}$ have the same units,
therefore $α t^{2}$ must be dimensionless for which
$α = \frac{1}{T ^{2}} = T^{- 2}$