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1.Units, Dimensions and Measurement
easy
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 $\alpha$
AIs a dimension less
Bhas dimensions $T^{-2}$
Chas dimensions of $P$
Dhas dimensions $T^2$
(AIPMT-1993)
Solution
$P = P _{0} e _{\alpha}\left(-\alpha t ^{2}\right)$
As we know both $P$ and $P _{0}$ are pressure so it have the same units, therefore $\alpha t ^{2}$ must be dimensionless.
$\alpha=\frac{1}{{ T }^{2}}= T ^{-2}$
So the dimension of $a$ is $\left[ T ^{-2}\right]$
As we know both $P$ and $P _{0}$ are pressure so it have the same units, therefore $\alpha t ^{2}$ must be dimensionless.
$\alpha=\frac{1}{{ T }^{2}}= T ^{-2}$
So the dimension of $a$ is $\left[ T ^{-2}\right]$
Standard 11
Physics
