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1.Units, Dimensions and Measurement
normal
The time dependence of a physical quantity $P$ is given by $P\, = \,{P_0}\,{e^{ - \alpha {t^2}}}$ where $\alpha $ is a constant and $t$ is the time then constant $\alpha $ is
ADimension less
BDimensions of $T^{-2}$
CDimensions of $P$
DDimensions of $T^2$
Solution
dimension of input of exponential function is zero
$ \Rightarrow \,[\alpha {t^2}]\, = \,1\, \Rightarrow \,[\alpha ]\, = \,\frac{1}{{[{t^2}]}}\, = \,{T^{ – 2}}$
$ \Rightarrow \,[\alpha {t^2}]\, = \,1\, \Rightarrow \,[\alpha ]\, = \,\frac{1}{{[{t^2}]}}\, = \,{T^{ – 2}}$
Standard 11
Physics
