A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume with time at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by

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Solution

The correct option is D
Rate of increase of volume is constant.
Hence,
$V = c t$ ( Here $c$ is constant)
$\frac{4}{3} π R^{3} = c t$
$\Rightarrow R \propto (t)^{1 / 3}$
$\Rightarrow R = R_{o} (t)^{1 / 3}$

Pressure inside bubble will be
$P = P_{0} + \frac{4 T}{R}$

$P = P_{0} + \frac{4 T}{R (t)^{1} / 3}$

only graph possible is option $d$

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A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume with time at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by

The correct option is D Rate of increase of volume is constant. Hence, V=ct ( Here c is constant) 43πR3=ct ⇒R∝(t)1/3 ⇒R=Ro(t)1/3 Pressure inside bubble will be P=P0+4TR P=P0+4TR(t)1/3 only graph possible is option d