The time dependence of a physical quantity p is given by p=p0e-at2, where α is constant and t is time. The constant α

Question

The time dependence of a physical quantity p is given by p=p0e-at2, where α is constant and t is time. The constant α (A) is dimensionless (B) has dimensions [T-2] (C) has dimensions [T2] (D) has dimensions of p

Tardigrade Admin · Accepted Answer

Given: p = p0e -α t2 α t2 is dimensionless ∴ [α ] = (1/[t2]) = (1/[T2]) = [T-2]

Q. The time dependence of a physical quantity $p$ is given by $p = p_{0} e^{- a t^{2}}$ , where $α$ is constant and $t$ is time. The constant $α$

is dimensionless

has dimensions $[T^{- 2}]$

has dimensions $[T^{2}]$

has dimensions of $p$

Given : $p = p_{0} e^{- α t^{2}}$
$α t^{2}$ is dimensionless
$∴ [α] = \frac{1}{[ t ^{2} ]} = \frac{1}{[ T ^{2} ]} = [T^{- 2}]$

Q. The time dependence of a physical quantity p is given by p=p0​e−at2, where α is constant and t is time. The constant α

is dimensionless

has dimensions [T−2]

has dimensions [T2]

has dimensions of p

Given : p=p0​e−αt2 αt2 is dimensionless ∴[α]=[t2]1​=[T2]1​=[T−2]

Q. The time dependence of a physical quantity $p$ is given by $p = p_{0} e^{- a t^{2}}$ , where $α$ is constant and $t$ is time. The constant $α$

has dimensions $[T^{- 2}]$

has dimensions $[T^{2}]$

has dimensions of $p$

Given : $p = p_{0} e^{- α t^{2}}$
$α t^{2}$ is dimensionless
$∴ [α] = \frac{1}{[ t ^{2} ]} = \frac{1}{[ T ^{2} ]} = [T^{- 2}]$