A physical quantity P is given by the relation. P=P0 e(-α t2) If t denotes the time, the dimensions of constant α are

Question

A physical quantity P is given by the relation. P=P0 e(-α t2) If t denotes the time, the dimensions of constant α are (A) [ T ] (B) [ T 2] (C) [ T -1] (D) [ T -2]

Tardigrade Admin · Accepted Answer

P=P0 e-α t2 The power of exponent is dimensionless, α t2=[ M 0 L 0 T 0] α=[ T -2]

Q. 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

$[T]$

$[T^{2}]$

$[T^{- 1}]$

$[T^{- 2}]$

$P = P_{0} e^{- α t^{2}}$
The power of exponent is dimensionless,
$α t^{2} = [M^{0} L^{0} T^{0}]$
$α = [T^{- 2}]$

Q. A physical quantity P is given by the relation. P=P0​e(−αt2) If t denotes the time, the dimensions of constant α are

[T]

[T2]

[T−1]

[T−2]