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 of P
D. has dimensions `[T^(2)]`

Answer

B

Explanation

`P = P_(0)e^(alpha t^(2))`
`alpha t^2` must be dimensionless
Thus dimensions of `alpha = (1)/(t^(2)) = [T^(-2)]`