IIT-JEE 2008 · Paper 1 · Physics Q38

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Paragraph for Question Nos. 38 to 40

A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac53\right)$ is trapped inside a liquid of density $\rho_\ell$ (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 $T_0$ , the height of the liquid is $H$ and the atmospheric pressure is $P_0$ (Neglect surface tension).

A container of liquid of height H open to the atmosphere (pressure P₀ at the top); a small gas bubble is at height y above the bottom.

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

Only the force of gravity

The force due to gravity and the force due to the pressure of the liquid

The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid

The force due to gravity and the force due to viscosity of the liquid

Answer and worked solution

Official answer: D

Forces on the bubble. The liquid's pressure on the bubble's surface is the buoyant force, so it must not be counted again. The remaining forces are the bubble's weight (gravity) and, since it moves through the liquid, viscous drag.

(D)

Topics:Buoyancy and Archimedes' principle Viscosity and Stokes' law

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IIT-JEE 2008 · Paper 1, Physics question 38