Question

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: Tiny drops of liquid resist deforming forces better than bigger drops. Reason: Excess pressure inside a drop is directly proportional to surface tension. (A) a (B) \(b\) (C) (D) d

Short answer

(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.

Step-by-step solution

Understanding deforming forces

Deforming forces are external forces that can change the shape of an object, in this case, a liquid drop. They can act on the drop through various mechanisms, such as gravity, pressure differences, or external stimuli.

Understanding the concept of excess pressure inside a drop

Excess pressure is the difference in pressure between the inside and the outside of a drop or bubble. It results from the surface tension, which is the force that acts along the surface of a liquid and tends to minimize its surface area. According to LaPlace's Law, excess pressure inside a spherical drop due to surface tension is given by the formula: \[ P_{excess} = \dfrac{2\gamma}{R} \] where \(\gamma\) is the surface tension of the liquid, and \(R\) is the radius of the drop. From this formula, we can see that the excess pressure is inversely proportional to the radius of the drop.

Comparing the resistance to deforming forces in tiny and bigger drops

When considering the resistance of drops to deformation, we must take into account both the excess pressure within the drop and the surface tension. Since excess pressure is inversely proportional to the radius, smaller drops (with smaller radii) will have a higher excess pressure. This higher excess pressure will make the drops more resistant to deforming forces.

Analyzing the given reason

The given reason states that excess pressure inside a drop is directly proportional to surface tension. From LaPlace's Law, we know this statement is true as excess pressure depends on surface tension: \[ P_{excess} = \dfrac{2\gamma}{R} \]

Determining the relationship between the assertion and the reason

Now that we have broken down the assertion and reason individually, we must determine whether the given reason is the correct explanation for the assertion. The assertion claims that tiny drops of liquid resist deforming forces better than bigger drops, which is true, as described in Step 3. The reason provided states that excess pressure inside a drop is directly proportional to the surface tension, which is also true, as seen from LaPlace's Law in Step 4. However, this reason does not completely explain why tiny drops resist deformation better than bigger drops, as it only addresses one aspect of the phenomenon (the relationship between excess pressure and surface tension). The inverse relation between excess pressure and the radius of the drop is crucial to understanding the full explanation. Based on the discussion above, the most accurate answer to the exercise is:

Answer

(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.

Key concepts

Deforming Forces

Deforming forces are intriguing because they directly affect the shape and structure of objects. Imagine a droplet of water; it's beautifully spherical, but when it falls or is squashed, changes occur. These changes are initiated by deforming forces.

Deforming forces can be caused by several factors:

• Gravity: Pulls the drop downwards, stretching it vertically.
• Pressure Differences: Variances either inside or outside the droplet can squeeze or expand it.
• External Stimuli: Such as wind or touch, can distort the droplet shape.

Understanding these forces helps us see why tiny droplets can be more resistant than larger ones. A smaller droplet has higher excess pressure, making it more stable against these deforming forces, as it withstands the external influences better due to its internal structure.

Excess Pressure

Excess pressure plays a crucial role in determining the behavior of liquid droplets. It occurs due to the phenomenon called surface tension, which tries to minimize the surface area of the liquid. In a droplet, this excess pressure is the additional pressure inside, compared to the surrounding environment.

Mathematically, excess pressure can be described by: \[ P_{excess} = \dfrac{2\gamma}{R} \] Where:

• \( \gamma \) represents the surface tension of the liquid.
• \( R \) is the radius of the droplet.

From this equation, it becomes clear that the excess pressure is inversely proportional to the radius of the drop. This means:

• Smaller drops have larger excess pressure compared to bigger ones.
• This high pressure makes smaller drops resist deformation.

Excess pressure is a remarkable property because it helps us understand the stability and shape-retaining capacity of small droplets.

Laplace's Law

Laplace's Law provides a powerful insight into how pressure behaves in microscopic systems, such as bubbles or droplets. This law connects surface tension and the geometry of a droplet with its internal pressure, reflecting how nature strives for equilibrium in these tiny systems.

The law is expressed by the same formula for excess pressure: \[ P_{excess} = \dfrac{2\gamma}{R} \] This relation is pivotal as it shows:

• Increased surface tension directly leads to increased excess pressure, as it's proportional.
• Decreased radius results in higher excess pressure, providing greater resistance to deformation.

Laplace’s Law helps in several applications, from understanding how raindrops form to how bubbles behave. It demonstrates why smaller drops rarely change shape under normal conditions due to the balance the law predicts. This interplay also explains technological processes that use droplets and bubbles, like inkjet printing or foaming agents in industrial applications.