A glass tube of uniform internal radius r has a valve separating the two identical ends…

Q: A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the value 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.

Numerical

(a) Air from end 1 flows towards end 2. No change in the volume of the soap bubbles

(b)Air from end 1 flows towards end 2. volume of the soap bubbles at end 1 decreases

(c) No change occurs

(d) Air from end 2 flows towards end 1. volume of the soap bubbles at ends 1 increases

Ans: (b)

Sol: $\large \Delta p_1 = \frac{4 T}{r_1}$ and $\large \Delta p_2 = \frac{4 T}{r_2}$

$\large r_1 < r_2 $

$\large \Delta p_1 > \Delta p_2$

Therefore , air will flow from 1 to 2 and volume of bubble at end 1 will decrease .