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1.Units, Dimensions and Measurement
hard
Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is
A
$k{\rho ^{1/2}}{a^{3/2}}{\bf{/}}\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) Let $n = k{\rho ^a}{a^b}{T^c}$ where $[\rho ] = [M{L^{ – 3}}],\;[a] = [L]$ and $[T] = [M{T^{ – 2}}]$
Comparing both sides, we get
$a = \frac{1}{2},\,b = \frac{3}{2}$ and $c = \frac{{ – 1}}{2}$
$\eta = \frac{{k{\rho ^{1/2}}{a^{3/2}}}}{{\sqrt T }}$
Standard 11
Physics
