Question

A soap bubble is blown with the help of a mechanical pump at the mouth of a tube. The pump produces constant increase in the radius per minute of the bubble, irrespective of its internal pressure. The graph between the excess pressure $p$ inside the soap bubble and time $t$ will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

We know that excess pressure inside the soap bubble is given by
$p=\frac{4T}{r}$, where $T$ is surface tension and $r$ is the radius of the bubble.
$\Rightarrow p\propto \frac{1}{r}$
$[$ surface tension of soap bubble is constant $]$
As radius of soap bubble increases with time at a constant rate,
$\therefore p\propto \frac{1}{t}$ .......(1)
Relation (1) is similar to the relation of a rectangular hyperbola i.e $y\propto \frac{1}{x}$.
Therefore, option $\left(a\right)$ is correct.