Askiitians Tutor Team
Last Activity: 5 Months ago
To tackle this question, we need to analyze the behavior of liquids in a capillary tube when a block of different density is placed on the liquid surface. This situation involves concepts from fluid mechanics, particularly capillarity and buoyancy. Let's break it down step by step.
Understanding Capillarity
Capillarity refers to the ability of a liquid to flow in narrow spaces without the assistance of external forces. This phenomenon occurs due to the cohesive forces within the liquid and the adhesive forces between the liquid and the walls of the tube. The height to which the liquid rises in the capillary tube is influenced by the liquid's density, the tube's radius, and the contact angle between the liquid and the tube material.
Initial Conditions
Initially, when the capillary tube is placed in a liquid of density d, the liquid rises to a height h. This height is determined by the balance of forces acting on the liquid column, which includes gravitational force and surface tension. The relationship can be expressed by the formula:
- h = (2 * γ * cos(θ)) / (ρ * g * r)
Where:
- γ = surface tension of the liquid
- θ = contact angle
- ρ = density of the liquid
- g = acceleration due to gravity
- r = radius of the capillary tube
Introducing the Block
Now, when a block of density D1 is placed on the liquid, we need to consider how this affects the liquid's height in the tube. If D1 is less than d (D1 < d), the block will float on the liquid due to buoyancy. The buoyant force acting on the block is equal to the weight of the liquid displaced by the block.
Analyzing the New Height
When the block is placed on the liquid, it will cause the liquid level in the capillary tube to change. The new height of the liquid in the tube is denoted as h1. The key point here is that since the block is less dense than the liquid, it will not sink completely, and the liquid will rise to a new equilibrium height.
Comparing Heights
Now, we need to determine the relationship between h1 and h. Since the block is floating, it displaces some volume of liquid, which leads to a rise in the liquid level. However, the rise will not exceed the original height h because the block's density is less than that of the liquid. Therefore, we can conclude:
Final Thoughts
In summary, when a block of density less than that of the liquid is placed on the surface, the height of the liquid in the capillary tube will indeed rise, but it will be less than the original height. Thus, the correct answer is h1 < h. This relationship illustrates the principles of buoyancy and capillarity effectively, showing how different densities interact in fluid systems.
