Properties of Matter 3 Question 1
7. 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 hemispherial soap bubble of radius $r$. End 2 has sub-hemispherical soap bubble as shown in figure.
Just after opening the valve.
(2008, 3M)
(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 bubble at end 1 decreases
(c) no change occurs
(d) air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases
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Answer:
Correct Answer: 7. (a)
Solution:
- Applying continuity equation at 1 and 2 , we have
$$ A _1 v _1=A _2 v _2 $$
Further applying Bernoulli’s equation at these two points, we have
$$ p _0+\rho g h+\frac{1}{2} \rho v _1^{2}=p _0+0+\frac{1}{2} \rho v _2^{2} $$
Solving Eqs. (i) and (ii), we have $v _2^{2}=\frac{2 g h}{1-\frac{A _2^{2}}{A _1^{2}}}$
Substituting the values, we have
$$ v _2^{2}=\frac{2 \times 10 \times 2.475}{1-(0.1)^{2}}=50 m^{2} / s^{2} $$
