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1.Units, Dimensions and Measurement
medium
If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is
A
$T = k\sqrt {\rho {r^3}/S} $
B
$T = k\sqrt {{\rho ^{1/2}}{r^3}/S} $
C
$T = k\sqrt {\rho {r^3}/{S^{1/2}}} $
D
None of these
Solution
(a) Let $T \propto {S^x}{r^y}{\rho ^z}$
by substituting the dimension of $[T] = [T]$
$[S] = [M{T^{ – 2}}],\,[r] = [L],\,[\rho ] = [M{L^{ – 3}}]$
and by comparing the power of both the sides
$x = – 1/2,\,y = 3/2,\,z = 1/2$
so $T \propto \sqrt {\rho {r^3}/S} \Rightarrow T = k\sqrt {\frac{{\rho {r^3}}}{S}} $
Standard 11
Physics
