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

Options

A. is dimensionless
B. has dimensions `[T^(-2)]`
C. has dimensions `[T^(2)]`
D. has dimensions of `P`

Answer

B

Explanation

`p = p_(0) exp (-alphat^(2))`
As powers of exponential quantity is dimesnionless, so `alphat^(2)` is dimensions.
or `alphat^(2) =` dimensionless `= [M^(0)L^(0)T^(0)]`
`:. alpha = (1)/(t^(2)) = (1)/([T^(2)]) = [T^(-2)]`