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Q.

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

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a

dimensionless

b

dimension of $t^{- 2}$

c

dimensions of P

d

dimension of $t^{2}$

answer is B.

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Detailed Solution

Here $α t^{2}$ is a dimensionless. Therefore, $α = \frac{1}{t^{2}}$ and has the dimension of $[T^{- 2}]$

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The time dependence of a physical quantity P is given by P=P0eαt2,where α is a constant and t is time. Then constant α is