Q 11-09-148JEE MainJEE Main 2019 (12 Jan, Shift 2)Medium
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:
Answer: (D) see figure
Volume grows uniformly, $\dfrac43\pi r^3 \propto t$, so $r \propto t^{1/3}$.
Pressure inside a soap bubble: $P = P_0 + \dfrac{4T}{r}$, so
$$P = P_0 + \frac{k}{t^{1/3}}$$
$P$ against $\dfrac{1}{t^{1/3}}$ is a straight line with a positive intercept $P_0$: graph (4).
Solution by Sreeraj P, M.Sc Physics