Paragraph: A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac{5}{3}\right)$ is trapped inside…

Paragraph: A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac{5}{3}\right)$ is trapped inside a liquid of density $\rho_1$ (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).
Question: As the bubble moves upwards, besides the buoyancy force the following forces are acting on it.
  1. Only the force of gravity
  2. The force due to gravity and the force due to pressure of the liquid
  3. The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
  4. The force due to gravity and the force due to viscosity of the liquid

Solution

As the bubble moves upwards, besides the buoyancy force (cause of which is pressure difference) only force of gravity and force of viscosity will act. $\therefore$ correct option is (d).

Asked in: JEE Advanced 2008 (Paper 1)

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