Question

A drop of liquid acquires a spherical shape because of (a) its tendency to maximize its surface area (b) its tendency to acquire minimum surface area (c) its viscous nature (d) none of these

Short answer

(b) its tendency to acquire minimum surface area.

Step-by-step solution

Understanding the Problem

We need to determine why a drop of liquid forms a spherical shape. To do this, we need to understand the forces at play when a liquid drop forms, focusing on surface tension and the shape that minimizes energy.

Basics of Surface Tension

Surface tension is a property of the liquid's surface that causes it to behave as if covered by a stretched elastic membrane. This leads the liquid to minimize its surface area for a given volume.

Connecting Spherical Shape to Surface Area

A sphere has the smallest possible surface area for a given volume. Therefore, to minimize surface area, a drop of liquid naturally forms a spherical shape due to surface tension.

Eliminating Incorrect Options

Option (a) suggests maximizing surface area, which is contrary to the behavior of liquids under surface tension. Option (c), the viscous nature, deals with internal friction and not shape. Option (d) does not offer a valid explanation. Thus, options (a), (c), and (d) are incorrect.

Choosing the Correct Answer

Based on the understanding that surface tension minimizes surface area, we conclude that the correct answer is (b), as a liquid drop forms a spherical shape due to its tendency to acquire minimum surface area.

Key concepts

Spherical Shape of Liquid Drops

Liquid drops tend to form a spherical shape due to the phenomenon known as surface tension. Imagine the surface of a liquid droplet acting like a stretched rubber membrane trying to contract. This tension arises from the cohesive forces between liquid molecules, striving to pull the surface into the most compact shape possible. For any given volume, the shape that achieves the smallest possible surface area is a sphere. That's why raindrops, for example, appear spherical.

The sphere minimizes the surface area for a specific volume, helping the liquid preserve energy. In a non-gravitational environment or when gravity's influence is negligible, the dominant factor shaping the drop is surface tension. As the molecules at the surface of the drop are pulled together tightly, they shape the liquid into a quick-to-find, compact form—the sphere.

Minimizing Surface Area

Minimizing surface area is a critical concept in understanding why liquid drops are spherical. A key aspect is the liquid's ability to naturally seek the smallest surface area possible for a given volume. This is due to surface tension, which forces the molecules on the surface to contract and pull inward.

Let's consider why this happens:

• Energy Conservation: The surface tension creates a pressure that drives the liquid to reduce its surface area and thereby stabilize its energy.
• Spheres in Geometry: Among all geometrical shapes, a sphere contains the maximum volume with the least surface area.
• Efficient Mechanics: In terms of mechanical efficiency, nature often favors shapes that are resistant to deformation and coincide with energy-efficient forms. Thus, drops minimize their surface area by adopting a spherical shape, conserving energy and achieving equilibrium.

Forces in Liquids

Forces in liquids, particularly the cohesive forces, play an integral part in the formation of a liquid drop. These forces act between molecules of the same substance and are responsible for various phenomena like surface tension.

Cohesive forces are the attractive forces between molecules in a liquid that keep them together. Due to these forces, the molecules at the surface are pulled inwards by the molecules below, which in turn create the surface tension.

Here's how these forces operate:

• Cohesion: This is the force that holds the liquid molecules together, making them 'stick'. It contributes to the droplet forming a compact shape.
• Adhesion: Although not the main focus in forming a droplet's shape, adhesive forces between a liquid and another surface play crucial roles in other liquid interactions.
• Surface Tension: As a result, surface tension becomes significant, acting to reduce the surface area and facilitating the spherical shape.
  
  When surface tension and cohesive forces work together, they create stable shapes like spheres in certain conditions, playing a fundamental role in the behavior of liquids.