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` is

Options

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

Answer

(b)

Explanation

`P = P_0 exp (- alpha t^2)`
As P and `P_0` have the same units, therefore `alpha t^2`
must be dimensionless for which `alpha = (1)/(T^2) = T^(-2)`