A glass tube of uniform internal radius has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. [2008]

Question

A glass tube of uniform internal radius $(r)$ has a valve separating the two identical ends. Initially, the valve is in a tightly closed position.

End 1 has a hemispherical soap bubble of radius $r$ . End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve, [2008]

Smart Achievers · Accepted Answer

(2)

We know that excess pressure in a soap bubble is inversely proportional to its radius, i.e., $P = \frac{4 T}{r}$

The soap bubble at end 1 has smaller radius as compared to the soap bubble at end 2 (given). Therefore excess pressure at 1 is more.

Hence, air flows from end 1 to end 2 and the volume of soap bubble at end 1 decreases.

Solution

1 air from end 1 flows towards end 2. No change in the volume of the soap bubbles

2 air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases

3 no changes occurs

4 air from end 2 flows towards end 1. volume of the soap bubble at end 1 increases

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