Question

The surface tension of soap solution is $ 0.005N{m^{ - 1}} $. If the diameter of the soap is 4cm, the excess pressure inside the soap bubble over that of the outside is _______ Pascal.
(A) $ 10 $
(B) $ 1.0 $
(C) $ 0.1 $
(D) $ 0.25 $

Answer 1

Hint: The pressure inside the bubble is more than the pressure outside. Using the diameter of the soap bubble and the value of the surface tension given in the question we can find the excess pressure by the formula, $ {P_{excess}} = \dfrac{{2 \times 2T}}{R} $.

Formula Used: The following formulas are used to solve this question.
 $\Rightarrow {P_{excess}} = \dfrac{{2 \times 2T}}{R} $, where $ {P_{excess}} $ is the excess pressure, $ T $ is the surface tension and $ R $ is the radius of the soap bubble.

Complete step by step answer
The surface tension is the magnitude of the force exerted parallel to the surface of a liquid divided by the length L of the line over which the force acts.
Given that the surface tension of soap solution is $ 0.005N{m^{ - 1}} $. We know that pressure inside the bubble is more than the pressure outside.
The excess pressure inside a soap bubble is given by the formula, $ {P_{excess}} = \dfrac{{2 \times 2T}}{R} $ where $ {P_{excess}} $ is the excess pressure, $ T $ is the surface tension and $ R $ is the radius of the soap bubble.
It is given that the diameter of the soap bubble is $ 4cm $ and the surface tension $ T = 0.005N{m^{ - 1}} $.
 $ \therefore $ The radius of the soap bubble $ R = \dfrac{4}{2} = 2cm $
Assigning the values to the given equation, we get,
 $ {P_{excess}} = \dfrac{{2 \times 2T}}{R} = \dfrac{{4 \times 0.005}}{{2 \times {{10}^{ - 2}}}}N{m^{ - 2}} $
 $ \Rightarrow {P_{excess}} = \dfrac{{0.02}}{{2 \times {{10}^{ - 2}}}} $
Therefore the excess pressure $ {P_{excess}} = 10Pa. $

$ \therefore $ The correct answer is Option D.

Note
Surface tension is a property that allows the surface of a liquid to behave somewhat as a trampoline does. When a person stands on a trampoline, the trampoline stretches downward a bit and, in so doing, exerts an upward elastic force on the person. This upward force balances the person’s weight. The surface of the water behaves in a similar way.