...........is the property by virtue of which the free surface of the liquid at rest behaves like a stretched elastic membrane tending to contract to occupy minimum surface area.

Answer

To solve the question, we need to identify the property of liquids that causes their free surface to behave like a stretched elastic membrane. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Concept of Surface Tension
- Surface tension is a physical property of liquids that arises from the cohesive forces between liquid molecules. It causes the surface of a liquid to behave like a stretched elastic membrane.

### Step 2: Identify the Behavior of Liquid at Rest
- When a liquid is at rest, the molecules at the surface experience a net inward force due to the attraction from the molecules below. This creates a tension at the surface.

### Step 3: Minimum Surface Area
- The liquid surface tries to minimize its surface area. This is because a smaller surface area corresponds to a lower energy state. The shape that provides the minimum surface area for a given volume is a sphere.

### Step 4: Real-World Example
- A common example of surface tension is a water droplet. When a droplet is formed, it takes on a spherical shape because this shape minimizes the surface area relative to its volume.

### Conclusion
- Therefore, the answer to the question is: **Surface tension** is the property by virtue of which the free surface of the liquid at rest behaves like a stretched elastic membrane tending to occupy minimum surface area.

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