Question 141 of 192

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:

ABCD

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Answer: (D)

$\dfrac{dV}{dt}=k$

$\Rightarrow V=kt$

$\Rightarrow \dfrac{4}{3}\pi {r}^{3}=kt$

$\Rightarrow r={\left(\dfrac{3k}{4\pi }\right)}^{\dfrac{1}{3}}{t}^{\dfrac{1}{3}}$

$P-{P}_{0}=\dfrac{4T}{r}$

$\Rightarrow P-{P}_{0}=4T.{\left(\dfrac{3k}{4\pi }\right)}^{\dfrac{1}{3}}.\dfrac{1}{{t}^{\dfrac{1}{3}}}$$\Rightarrow P=4T.{\left(\dfrac{3k}{4\pi }\right)}^{\dfrac{1}{3}}.\dfrac{1}{{t}^{\dfrac{1}{3}}}+{P}_{0}$