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The time dependence of a physical quanti...

The time dependence of a physical quantity P is given by `P=P_(0) exp (-alpha t^(2))`, where `alpha` is a cosntant and t is time. The constant `alpha`

A

is dimensionless

B

has dimensions [`T^(-2)`

C

has dimensions of P

D

has dimensions `[T^(2)]`

Text Solution

Verified by Experts

The correct Answer is:
B
`P = P_(0)e^(alpha t^(2))`
`alpha t^2` must be dimensionless
Thus dimensions of `alpha = (1)/(t^(2)) = [T^(-2)]`
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ALLEN -PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT -EXERCISE-I DIMENSIONS
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