1.Units, Dimensions and Measurement
hard

$ P = \frac{\alpha }{\beta }{e^{ - \frac{{\alpha Z}}{{k\theta }}}} $ સૂત્રમા $P$ દબાણ, $Z$ અંતરં, તાપમાન અને $k$ બોલ્ટ્‍ઝમેન અચળાંક હોય,તો $\beta$નું પારિમાણીક સૂત્ર શું થાય?

A

$ [{M^0}{L^2}{T^0}] $

B

$ [{M^1}{L^2}{T^1}] $

C

$ [{M^1}{L^0}{T^{ - 1}}] $

D

$ [{M^0}{L^2}{T^{ - 1}}] $

(IIT-2004)

Solution

(a) In given equation, $\frac{{\alpha z}}{{k\theta }}$ should be dimensionless

$\therefore \alpha = \frac{{k\theta }}{z} \Rightarrow [\alpha ] = \frac{{[M{L^2}{T^{ – 2}}{K^{ – 1}} \times K]}}{{[L]}} = [ML{T^{ – 2}}]$

and $P = \frac{\alpha }{{ \beta }} \Rightarrow [\beta ] = \left[ {\frac{\alpha }{p}} \right] = \frac{{[ML{T^{ – 2}}]}}{{[M{L^{ – 1}}{T^{ – 2}}]}} = [{M^0}{L^2}{T^0}]$.

Standard 11
Physics

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