Question

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 1

Given that,

A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate.

We know that,

The pressure difference in soap bubble is

$\Delta P=\dfrac{4T}{r}$.....(I)

Where, T = temperature

r = radius

We know that,

The relation between volume and time

$V=ct$

$\dfrac{4}{3}\pi r^3=ct$

Where, r = radius

t = time

$r^3=\dfrac{3ct}{4\pi}$

$r=kt^{\frac{1}{3}}$

The  radius of soap bubble increases with time.

Where, $k= \dfrac{3c}{4\pi}$

Now, put the value of r in equation (I)

$\Delta P=\dfrac{4T}{kt^{\frac{1}{3}}}$

$P\propto\dfrac{1}{t^{\frac{1}{3}}}$

Hence, The pressure will be decrease with time.

Here, no correct option in graph.  

Answer 2

Answer:

Option (c) is the correct answer.

$thanks$