1.Units, Dimensions and Measurement
hard

यदि आवृत्ति, घनत्व $(\rho )$ लंबाई $(a)$ तथा पृष्ठ-तनाव $(T)$ का फलन हो तो इसका मान होगा

A

$k\,{\rho ^{1/2}}{a^{3/2}}/\sqrt T $

B

$k\,{\rho ^{3/2}}{a^{3/2}}/\sqrt T $

C

$k\,{\rho ^{1/2}}{a^{3/2}}/{T^{3/4}}$

D

$k\,{\rho ^{1/2}}{a^{1/2}}/{T^{3/2}}$

Solution

(a) माना $n = k{\rho ^a}{a^b}{T^c}$ जहाँ $[\rho ] = [M{L^{ – 3}}],\;[a] = [L]$ तथा $[T] = [M{T^{ – 2}}]$

दोनों ओर विमाओं की तुलना करने पर

$a = \frac{1}{2},\,b = \frac{3}{2}$ तथा $c = \frac{{ – 1}}{2}$

$⇒$ $\eta = \frac{{k{\rho ^{1/2}}{a^{3/2}}}}{{\sqrt T }}$

Standard 11
Physics

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