Question

The time dependence of physical quantity P is found to be of the form $P = P_{0}e^{- \alpha t^{2}}$Where ‘t’ is the time and α is some constant.

• A. Be dimensionless
• B. Have dimensions of T^–2
• C. Have dimensions of P
• D. Have dimensions of P multiplied by T^–

Answer 1

Answer: (B)

Have dimensions of T^–2

Answer 2

Since in e^x x is dimensionless

∴ In $e^{- \alpha t^{2}}$; at² should be dimensionless

$\alpha t^{2} = M^{0}L^{0}T^{0}$

$\alpha = M^{0}L^{0}T^{0}$