Question

If the radius of a soap bubble is four times that of another, then the ratio of their pressure will be
A. 1 : 4
B. 4 : 1
C. 16 : 1
D. 1 : 16

Answer 1

Hint:We are given that the radius of a bubble is four times than that of another and we have to find the ratio of their pressures. By putting the values of excess pressure for two bubbles with different radius and comparing the values, we are able to get the ratio of the pressures.

Formula Used:
The excess pressure $\Delta P$inside a soap bubble is,
$\Delta P=\dfrac{4T}{R}$
Where T is the surface tension on the soap and R is the radius of the soap bubble.

Complete step by step solution:
Consider that the excess pressure inside the first and second soap bubble is $\Delta {{P}_{1}}$ and $\Delta {{P}_{2}}$ respectively. Let the radii and the volume of first and second soap bubbles are ${{R}_{1}}$ and ${{R}_{2}}$ and the volumes be ${{V}_{1}}$ and ${{V}_{2}}$ respectively. We are given that the radius of a soap bubble is four times that of another. And we know $\Delta P\propto \dfrac{1}{R}$.

Now we write the above relation for two soap bubbles,
$\dfrac{\Delta {{P}_{1}}}{\Delta {{P}_{2}}}=\dfrac{{{R}_{2}}}{{{R}_{1}}} \\ $
Now we substitute ${{R}_{1}}=4{{R}_{2}}$ in the above equation, we get;
$\dfrac{\Delta {{P}_{1}}}{\Delta {{P}_{2}}}=\dfrac{{{R}_{2}}}{4{{R}_{2}}} \\ $
Solving the above equation, we get
$\Delta {{P}_{2}}=4\Delta {{P}_{1}} \\ $
$\therefore \dfrac{\Delta {{P}_{1}}}{\Delta {{P}_{2}}}=\dfrac{1}{4}$
Hence the ratio of excess pressure of the soap bubble is 1 : 4 when the radius is four times than that of another.

Hence, option A is the correct answer.

Note: In a liquid, the surface tension which holds the molecules is very strong and we are not able to get the bubbles. When we add the detergent, it can lower the surface tension of the liquid and bubbles can form due to low surface tension.