1.Units, Dimensions and Measurement
hard

व्यंजक $P = \frac{\alpha }{\beta }{e^{ - \frac{{\alpha Z}}{{k\theta }}}}$ में $P$ दाब, $ Z$ दूरी, $k$ बोल्ट्जमैन स्थिरांक एवं तापक्रम दर्शाता है तो का विमीय सूत्र होगा

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) दिये गये समीकरण में, $\frac{{\alpha z}}{{k\theta }}$ विमाहीन होना चाहिये,

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

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

Standard 11
Physics

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