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1.Units, Dimensions and Measurement
easy
एक समी. में $P$ का समय के साथ संबंध इस प्रकार है $P = P _{0} \exp \left(-\alpha t ^{2}\right)$ जहां $\alpha$ एक नियतांक है, तो $\alpha$ की विमा होगी
Aकोई विमा नहीं
B$T ^{-2}$ की विमा
C$P$ की विमा
D$T ^{2}$ की विमा
(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
