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

Options

A.
B.
C.
D.

Answer

C

Explanation

The excess pressure `(DeltaP)` inside the soap bubble is
` Delta P = (4T)/r i.e Delta P prop 1/r or dP xx r = 4T ` ,
But the volume of the bubble is also increasing with time .
i.e the radius of the bubble is also increasing with time.
Thus ` r prop t " " :. Delta P prop 1/t`
` :. ` The graph between `DeltaP` and t will be a rectangular byperbola as shown in fig (c ) .
This is similar to graph between h and r ` [ h prop 1/r]` and hr = constant