The time dependence of a physical quantity P is given by P - P0e- t2- where - is a constant and t is time- Then constant - is - has

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Dimensional Analysis

The time depe...

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

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Dimensions of

T^{- 2}

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Dimensions of P

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Dimensions of

T^{2}

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Solution

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

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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 / has

The correct option is B Dimensions of T−2P=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

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