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Grade upto college level Mechanics

Figure 13-15 shows a circular glass tube fastened to a vertical wall. The tube is filled with water except for an air bubble that is temporarily at rest at the bottom of the tube. Discuss the subsequent motion of the bubble in terms of energy transfers. Do so both neglecting viscous and frictional forces and taking them fully into account.
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

Profile image of Shane Macguire
11 Years agoGrade upto college level
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1 Answer

Profile image of Deepak Patra
11 Years ago
Initially assume that, there is no water in the tube. When the tube is filled with water, the kinetic energy of the water will transfer to the bubble and will cause the bubble to move in the absent of viscous and frictional force. If there is presence of viscous and frictional forces, then the bubble will come to rest in the tube after some time.