A small spherical monoatomic ideal gas bubble (γ=35) is trapped inside a liquid of density ρℓ (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 T0, the height of the liquid is H and the atmospheric pressure is P0 (Neglect surface tension).
As the bubble moves upwards, besides the buoyancy force the following forces are acting on it
(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✓ Correct
Answer: (D)
Solution
The buoyancy force is the net result of pressure forces from the liquid acting on the bubble's surface. Besides buoyancy, the bubble experiences gravity (its weight) and viscous drag from the liquid as it moves. The pressure forces are already accounted for in the buoyancy force, so the additional forces are gravity and viscosity.
JEE Advanced · 2008 · 13 Apr 2008 · Paper 1 · Single correct option
