Question

A physical quantity $P$ is given by the relation. $P=P_{0} e^{\left(-\alpha t^{2}\right)}$ If $t$ denotes the time, the dimensions of constant $\alpha$ are

• A. $[ T ]$
• B. $\left[ T ^{2}\right]$
• C. $\left[ T ^{-1}\right]$
• D. $\left[ T ^{-2}\right]$

Answer 1

Answer: (D)

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