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:

  1. Applying continuity equation at 1 and 2 , we have

A1v1=A2v2

Further applying Bernoulli’s equation at these two points, we have

p0+ρgh+12ρv12=p0+0+12ρv22

Solving Eqs. (i) and (ii), we have v22=2gh1A22A12

Substituting the values, we have

v22=2×10×2.4751(0.1)2=50m2/s2



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