
Two bubbles A and B (A > B) are joined through a narrow tube. Then
A. The size of A will increase
B. the size of B will increase
C. the size of B will increase until the pressure equals
D. none of these
Answer
161.7k+ views
Hint: We are given the two bubbles of different radii which are joined through a narrow tube. With the help of the formula of pressure inside a bubble $P={{P}_{0}}+\dfrac{4S}{R}$ we see that if the radius increases, pressure decreases. So the larger bubble will try to grow more in size by reducing the size of the smaller bubble.
Formula used:
The pressure inside the soap bubble is given by
$P={{P}_{0}}+\dfrac{4S}{R}$
Where R is the radius of the bubble, $S$ is the surface tension and $P_0$ is the atmospheric pressure.
Complete step by step solution:
We know a soap bubble has two surfaces, the outer surface and the inner surface. There exists a pressure difference between these two pressures and the pressure inside the bubbles is always greater than the pressure outside the bubble. The pressure inside the soap bubble is given by,
$P={{P}_{0}}+\dfrac{4S}{R}$
We can see that the $P\propto \dfrac{1}{R}$. That is P is inversely proportional to R Hence as the size of the soap bubble increases the pressure inside the bubble decreases. So the bubble always tries to get a large size by decreasing the pressure inside the bubble.
Now when we are given two bubbles A and B which are joined through a narrow tube, then the larger bubble (A) tries to increase its size by decreasing the pressure. Therefore, the air will flow from the smaller bubble ( B ) to the larger bubble (A) and the size of the larger bubble (A) increases.
Thus, option A is the correct answer.
Note: Remember that when the two bubbles of different radius are joined, the pressure inside the bubble causes the bubble to expand more and the smaller bubble causes it to shrink.
Formula used:
The pressure inside the soap bubble is given by
$P={{P}_{0}}+\dfrac{4S}{R}$
Where R is the radius of the bubble, $S$ is the surface tension and $P_0$ is the atmospheric pressure.
Complete step by step solution:
We know a soap bubble has two surfaces, the outer surface and the inner surface. There exists a pressure difference between these two pressures and the pressure inside the bubbles is always greater than the pressure outside the bubble. The pressure inside the soap bubble is given by,
$P={{P}_{0}}+\dfrac{4S}{R}$
We can see that the $P\propto \dfrac{1}{R}$. That is P is inversely proportional to R Hence as the size of the soap bubble increases the pressure inside the bubble decreases. So the bubble always tries to get a large size by decreasing the pressure inside the bubble.
Now when we are given two bubbles A and B which are joined through a narrow tube, then the larger bubble (A) tries to increase its size by decreasing the pressure. Therefore, the air will flow from the smaller bubble ( B ) to the larger bubble (A) and the size of the larger bubble (A) increases.
Thus, option A is the correct answer.
Note: Remember that when the two bubbles of different radius are joined, the pressure inside the bubble causes the bubble to expand more and the smaller bubble causes it to shrink.
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