Question

If the surface tension of a soap solution is 0.03 MKS units, then the excess of pressure inside a soap bubble of diameter 6 mm over the atmospheric pressure will be
A. Less than 40 $N/{{m}^{2}}$
B. Greater than 40 $N/{{m}^{2}}$
C. less than 20 $N/{{m}^{2}}$
D. Greater than 20 $N/{{m}^{2}}$

Answer 1

Hint: In this question, we have given the surface tension and we have to find the excess pressure inside the soap bubble. We know the pressure above the atmospheric pressure in a soap bubble can be written in the form of a soap bubble and its diameter. By putting the values in the identity and solving them, we are able to get our desirable answer.

Formula used:
the formula for excess pressure inside the soap bubble is,
$\Delta P=\dfrac{4\sigma }{R}$
Where $\sigma $ is the surface tension and R is the radius of the bubble.

Complete step by step solution:
Given the diameter of the soap bubble is 6 mm.
Then the radius of soap bubble = $\dfrac{D}{2}$= $\dfrac{6}{2}$= $3\,mm$
The amount of pressure exists inside the bubble is $\Delta P=0.03\,MKS$
We know the formula for excess pressure inside the soap bubble is,
$\Delta P=\dfrac{4\sigma }{R} \\ $
Now we will substitute the value of R and $\sigma $ in the above equation, we get
$\Delta P=\dfrac{4\times 0.03}{3} \\ $
Then $\sigma =40\,N/{{m}^{2}}$
Hence the surface tension of the soap bubble is greater than $40\,N/{{m}^{2}}$.

Thus, option B is the correct answer.

Note: The formula for excess pressure is formulated using the condition of equilibrium for the forces acting on the bubble. Surface tension and the force due to pressure are the forces which are acting on the soap bubble.