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Properties of Matter question

2008 · Shift 1 · Q61
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Properties of Matter question

2008 · Shift 1 · Q61

JEE AdvancedPhysicsProperties of MatterMCQ+3 / −1
A small spherical monoatomic ideal gas bubble (γ=53)\left( {\gamma = {5 \over 3}} \right)(γ=35​) is trapped inside a liquid of density ρ1\rho_1ρ1​ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T 0_00​, the height of the liquid is H and the atmospheric pressure is P 0_00​ (Neglect surface tension) IIT-JEE 2008 Paper 1 Offline Physics - Properties of Matter Question 9 English ComprehensionAs the bubble moves upwards, besides the buoyancy force the following forces are acting on it
  1. A
    Only the force of gravity
  2. B
    The force due to gravity and the force due to the pressure of the liquid
  3. C
    The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
  4. D
    The force due to gravity and the force due to viscosity of the liquid
View written solutionFree

Correct answer: D

  1. Identify all external forces on the bubble

A gas bubble moving upward in a liquid can experience:

  • Buoyant force upward due to pressure difference in the liquid
  • Weight (gravity) of the gas inside the bubble downward
  • Viscous drag due to relative motion between bubble and liquid, opposite to motion
  • Pressure forces exerted by the surrounding liquid on the bubble surface

The question says: "besides the buoyancy force", which means we should list other forces apart from buoyancy.

  1. Understand the role of pressure force

The liquid exerts pressure on the bubble from all sides. If we consider the net effect of all these pressure forces over the bubble surface, their resultant is exactly the buoyant force.

So, the net force due to liquid pressure is not something additional to buoyancy. It is already accounted for as buoyancy.

Hence, if buoyancy is excluded, we should not separately include pressure force again.

  1. Other actual forces acting on the bubble

Now, excluding buoyancy, the remaining forces are:

  • Gravity: the bubble contains gas, so it has mass and therefore weight.
  • Viscous force: as the bubble rises through the liquid, the liquid opposes its motion by viscosity.

Thus, besides buoyancy, the bubble experiences:

gravity+viscous drag\text{gravity} + \text{viscous drag}gravity+viscous drag

  1. Check options

  • A: Only the force of gravity
    Incorrect, because viscous drag also acts while the bubble moves upward.

  • B: The force due to gravity and the force due to the pressure of the liquid
    Incorrect, because the net pressure force is the buoyant force itself, already excluded.

  • C: The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
    Incorrect, because pressure force is not separate from buoyancy.

  • D: The force due to gravity and the force due to viscosity of the liquid
    Correct.

  1. Final answer

The correct option is:

D\boxed{\text{D}}D​

  1. Comparison with stored answer

Stored correct answer: D
Derived answer: D

So, the derived answer agrees with the stored answer.

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