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The time of oscillation of a small drop of liquid under surface tension depends upon density $ρ$ , radius r and surface tension s, as $T \propto ρ^{a} s^{b} r^{c}$ , then the descending order of a, b and c is

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a > b > c

a > c > b

b > a > c

c > a > b

answer is D.

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Detailed Solution

$[T] = {[{ML}^{- 3}]}^{a} {[{MT}^{- 2}]}^{b} {[L]}^{c}$

$[T] = [M^{a + b} L^{- 3 a + c} T^{- 2 b}]$

$- 2 b = 1 \Rightarrow b = - \frac{1}{2}$ ;

$a + b = 0 \Rightarrow a = - b = \frac{1}{2}$ ;

$- 3 a + c = 0 \Rightarrow c = \frac{3}{2}$

$∴ c > a > b$

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