Question

The time dependence of a physical quantity $P$ is given by $P=P_{0}exp(-\alpha t^2)$, where t is time and $\alpha$ is a constant and____________

• A. is dimensionless
• B. has dimensions $T^{-2}$
• C. has dimensions of $P$
• D. has dimensions $T^2$

Answer 1

The correct option is B has dimensions $T^{-2}$

Since power of exponent must be dimensionless, hence $\left[\alpha \right]T^2$ must be dimensionless. Hence $\left[\alpha \right]=T^{-2}$.