Question

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

Short answer

The correct answer is (C) The force due to gravity, the force due to the pressure of the liquid, and the force due to viscosity of the liquid.

Step-by-step solution

Analyze the forces acting on a bubble in a liquid

When a bubble rises through a liquid, it experiences several forces. The buoyancy force helps the bubble rise by countering the force of gravity. Gravity always acts on the bubble, pulling it downwards. The pressure of the liquid also exerts a force on the bubble, which changes with depth due to the hydrostatic pressure gradient. Additionally, as the bubble moves through the liquid, it encounters resistance due to the liquid's viscosity, which is the force due to viscosity.

Identify the correct combination of forces

Given the analysis, the correct forces acting on a bubble while it moves upwards in a liquid are: the force due to gravity, the force due to the pressure of the liquid, and the force due to the viscosity of the liquid. Therefore, option (C) is correct because it includes all three forces.

Key concepts

Force of Gravity

The force of gravity is a fundamental concept that students frequently encounter in physics. This force is the attraction between any two objects that have mass. On Earth, it's what gives objects weight and causes them to fall towards the ground when dropped. Its formula is given by Newton's law of universal gravitation:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( F \) is the force of gravity, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the objects, and \( r \) is the distance between their centers. In the context of the problem, the force of gravity acts on the bubble and opposes the buoyancy force, pulling it downward through the liquid. Understanding this force is vital to explaining why bubbles rise: they're essentially in a tug-of-war with gravity, with buoyancy often winning the battle because the bubble is lighter than the surrounding fluid.

Pressure of Liquid

When studying the behavior of liquids, it's important to understand the concept of pressure. Pressure in a liquid is exerted in all directions and increases with depth. This relation is given by the equation :
\[ P = P_0 + \rho gh \]
where \( P \) is the pressure at depth, \( P_0 \) is the surface pressure, \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( h \) is the depth below the surface. For an object submerged in a liquid, like a bubble, the liquid exerts a force due to this pressure. The key to grasping this concept lies in picturing how this force is applied—it's an all-encompassing squeeze that comes from every direction. In the rising bubble's case, the lower pressure at higher points helps push it upward, adding to the bubble's upward movement alongside buoyancy.

Viscosity of Liquid

Viscosity is a liquid's measure of resistance to flow, often thought of as its 'thickness'. For example, honey has a higher viscosity than water. The higher the viscosity, the more resistance an object moving through the liquid encounters. This resistance force is crucial when considering the movement of objects in fluids, including bubbles. Viscosity can be described mathematically by the formula:
\[ F_{\text{visc}} = 6\pi r \eta v \]
where \( F_{\text{visc}} \) is the frictional force due to viscosity, \( r \) is the radius of the object moving through the liquid, \( \eta \) is the liquid's viscosity, and \( v \) is the velocity of the object through the liquid. Understanding viscosity is helpful since it provides another piece of the puzzle explaining why some bubbles rise slowly while others ascend quickly, depending on the liquid's viscosity they are moving through.