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Physics-

General

Easy

Question

If $T$ is surface tension of soap solution, the amount of work done in blowing a soap bubble from a diameter $D$ to a diameter $2 D$ is

$2 π D^{2} T$
$4 π D^{2} T$
$6 π D^{2} T$
$8 π D^{2} T$

The correct answer is: $6 pi blank D to the power of 2 end exponent T$

Work done=(increase in surface are(a) $cross times$ surface tension
$equals 2 cross times open square brackets 4 pi open parentheses fraction numerator 2 D over denominator 2 end fraction close parentheses to the power of 2 end exponent minus 4 pi open parentheses fraction numerator D over denominator 2 end fraction close parentheses to the power of 2 end exponent close square brackets cross times T$
(Since for sap bubble, there are two free surfaces)
$equals 2 cross times open parentheses 4 pi D to the power of 2 end exponent minus pi D to the power of 2 end exponent close parentheses T equals 6 pi D to the power of 2 end exponent T$

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