JEE PYQ: Mechanical Properties Of Fluids Question 33
Question 33 - 2019 (12 Jan 2019 Shift 1)
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:
(1) Graph showing $P$ vs $\frac{1}{t}$ as a decreasing curve
(2) Graph showing $P$ vs $\log(t)$ as a decreasing straight line
(3) Graph showing $P$ vs $t$ as a decreasing curve
(4) None
Show Answer
Answer: (4) None
Solution
$V = ct$, $\frac{4}{3}\pi r^3 = ct$ $\Rightarrow r \propto t^{1/3}$ $P = P_0 + \frac{4T}{r} \propto P_0 + \frac{4T}{kt^{1/3}}$ $P = P_0 + c’\left(\frac{1}{t^{1/3}}\right)$ This matches graph (4).
BETA
