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-T-T-2-T-1-T-2-

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Given-P-P0e-x2212-x3B1-t2-As we know- both P and P0 are pressure- it have the same units- Therefore- -x3B1-t2 must be dimensionless for which-x3B1-1T2-T-x2212-2So the dimension of -x3B1- is -T-x2212-2-

A physical quantity $P$ is given by the relation, $P = P_{0} e^{(- α t^{2})}$ . If $t$ denotes the time, the dimensions of constant $α$ are
$[T]$
$[T^{2}]$
$[T^{- 1}]$
$[T^{- 2}]$

Given,

$P = P_{0} e^{(- α t^{2})}$

As we know, both $P$ and $P_{0}$ are pressure, it have the same units. Therefore, $α t^{2}$ must be dimensionless for which,

$α = \frac{1}{T^{2}} = T^{- 2}$

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

A physical quantity P is given by the relation, P=P0e(−αt2). If t denotes the time, the dimensions of constant α are[T][T2][T−1][T−2]

Given,P=P0e(−αt2)As we know, both P and P0 are pressure, it have the same units. Therefore, αt2 must be dimensionless for which,α=1T2=T−2So the dimension of α is [T−2].

A physical quantity $P$ is given by the relation, $P = P_{0} e^{(- α t^{2})}$ . If $t$ denotes the time, the dimensions of constant $α$ are
$[T]$
$[T^{2}]$
$[T^{- 1}]$
$[T^{- 2}]$

Given,

$P = P_{0} e^{(- α t^{2})}$

As we know, both $P$ and $P_{0}$ are pressure, it have the same units. Therefore, $α t^{2}$ must be dimensionless for which,

$α = \frac{1}{T^{2}} = T^{- 2}$

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