The liquid drop of density P, radius r and surface tension $σ$ oscillates with time period T Which of the following expression for T² is correct

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${ρr}^{3} / σ$

$r^{3} σ / ρ$

none of the above

$ρσ / r^{3}$

answer is A.

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Detailed Solution

$\begin{array}{l} T^{2} = ρ^{a} r^{b} σ^{c} = {[{ML}^{- 3}]}^{a} {[L]}^{b} {[{MT}^{- 2}]}^{c} \\ = [M^{a + c} L^{- 3 a + b} T^{- 2 c}] \end{array}$
$∴ a + c = 0, - 3 a + b = 0 and - 2 c = 2 .$
Hence ,a =1 ,b = 3 and c = -1

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