The time dependence of a physical quantity $P$ is given by $P = P_{0} e^{- α t^{2}}$ , where $α$ is a constant and t is time. Then constant $α$ is / has
Dimensionless
Dimensions of $T^{- 2}$
Dimensions of P
Dimensions of $T^{2}$

Question

The time dependence of a physical quantity $P$ is given by $P = P_{0} e^{- α t^{2}}$ , where $α$ is a constant and t is time. Then constant $α$ is / has
Dimensionless
Dimensions of $T^{- 2}$
Dimensions of P
Dimensions of $T^{2}$

Toppr Admin · Accepted Answer

P-P0e-x2212-x3B1-t2-x3B1-t2 must be dimension less in-xA0-e-x2212-x3B1-t2-x21D2-dim-x3B1-t2-M0L0T0-x21D2-dim-x3B1-M0L0T0T2-x2234-xA0-xA0-dim-x3B1-M0L0T-x2212-2

The time dependence of a physical quantity P is given by P=P0e−αt2, where α is a constant and t is time. Then constant α is / hasDimensionlessDimensions of T−2Dimensions of PDimensions of T2

P=P0e−αt2αt2 must be dimension less in e−αt2⇒dim(αt2)=M0L0T0⇒dim(α)=M0L0T0T2∴ dim(α)=M0L0T−2

The time dependence of a physical quantity $P$ is given by $P = P_{0} e^{- α t^{2}}$ , where $α$ is a constant and t is time. Then constant $α$ is / has
Dimensionless
Dimensions of $T^{- 2}$
Dimensions of P
Dimensions of $T^{2}$

$P = P_{0} e^{- {α t}^{2}}$
${α t}^{2}$ must be dimension less in $e^{- {α t}^{2}}$
$\Rightarrow d i m ({α t}^{2}) = M^{0} L^{0} T^{0} \Rightarrow d i m (α) = \frac{M^{0} L^{0} T^{0}}{T^{2}}$
$∴$ $d i m (α) = M^{0} L^{0} T^{- 2}$