Properties of Matter 4 Question 16
18. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it.
$(2008,4$ M)
(a) Only the force of gravity
(b) The force due to gravity and the force due to the pressure of the liquid
(c) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
(d) The force due to gravity and the force due to viscosity of the liquid
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Answer:
Correct Answer: 18. $\frac{d Q}{d t} \propto r^{5}$
Solution:
- Surface Tension force $=2 \pi b \times 2 T \sin \theta$
Mass of the air per second entering the bubble $=\rho A v$
Momentum of air per
$=$ Force due to air $=\rho A v^{2}$
The bubble will separate from the tube when force due to moving air becomes equal to the surface tension force inside the bubble.
$2 \pi b \times 2 T \sin \theta=\rho A v^{2}$
putting $\sin \theta=\frac{b}{r}, A=\pi b^{2}$ and solving, we get
$$ r=\frac{4 T}{\rho v^{2}} $$
