The time dependence of physical quantity P is found to be of the form P - -2- where -t- is the time and - is some constant- Then the constant - will

From the given expression: P = 𝑃_𝑜𝑒^−𝛼𝑡^2 Here, the exponent of e, cannot have any dimensions. ∴ [α]=[t^2]^ 1 [α]=[T^ 2] nbsp; nbsp; ...

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Standard XI

Physics

Limitation of Dimensional Analysis

The time depe...

Question

The time dependence of physical quantity $P$ is found to be of the form $P = P_{o} e^{- α t^{2}}$ , where $‘ t^{'}$ is the time and $α$ is some constant. Then the constant $α$ will

be dimensionless

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have dimensions of

T^{- 2}

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have dimensions of

P

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have dimensions of

P

multiplied by

T^{- 2}

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Solution

The correct option is B have dimensions of $T^{- 2}$
From the given expression:
$P = P_{o} e^{- α t^{2}}$

Here, the exponent of $e$ , cannot have any dimensions.
$∴ [α] = [t^{2}]^{- 1}$
$[α] = [T^{- 2}]$

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The time dependence of physical quantity P is found to be of the form P=Poe−αt2, where ‘t′ is the time and α is some constant. Then the constant α will

The correct option is B have dimensions of T−2From the given expression: P=Poe−αt2 Here, the exponent of e, cannot have any dimensions. ∴[α]=[t2]−1 [α]=[T−2]

The time dependence of physical quantity $P$ is found to be of the form $P = P_{o} e^{- α t^{2}}$ , where $‘ t^{'}$ is the time and $α$ is some constant. Then the constant $α$ will

The correct option is B have dimensions of $T^{- 2}$
From the given expression:
$P = P_{o} e^{- α t^{2}}$

Here, the exponent of $e$ , cannot have any dimensions.
$∴ [α] = [t^{2}]^{- 1}$
$[α] = [T^{- 2}]$