LEVELJEE Main

Animated Solution for Physics - Properties of Solids and Liquids: A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times 1 0^{- 2} N$ (see figure). The length of the slider is $30 cm$ and its weight negligible. The surface tension of the liquid film is

Select Answer:

Visualized Solution

Visualizing the Setup

Given:
$W = 1.5 \times 1 0^{- 2} N$
$L = 30 cm = 0.3 m$

Equilibrium Condition

At equilibrium:
$F_{upward} = F_{downward}$

Surface Tension Force

Force due to surface tension:
$F_{S} = S \times (2 L)$
where $S$ is the surface tension and $2 L$ accounts for the two surfaces.

Formulating the Equation

$2 L \cdot S = W$
$S = \frac{W}{2 L}$

Substituting Values

$S = \frac{1.5 \times 1 0 ^{- 2}}{2 \times 0.3}$

Simplifying Denominator

$S = \frac{1.5 \times 1 0 ^{- 2}}{0.6}$

Final Answer

$S = 2.5 \times 1 0^{- 2} N/m$
$S = 0.025 N/m$

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The Sigma Insight: Surface Tension and Capillary Action

Solution Diagram

The Setup

Imagine a delicate, shimmering liquid film stretched across a U-shaped wire frame. At the bottom of this film, a light slider is free to move up and down. Suspended from this slider is a small weight, pulling it downwards with a force of

W = 1.5 \times 1 0^{- 2} N

Despite this downward pull, the slider doesn't fall. It hangs in perfect equilibrium. Why? Because the surface tension of the liquid film is pulling it right back up!

The Hidden Trap

Two Surfaces

When dealing with liquid films, there is a classic trap that catches many students off guard. A film is not just a single sheet of liquid; it has two free surfaces—one facing you, and one on the back.

Because surface tension acts along the boundary of the liquid, both the front and back surfaces exert an upward force on the slider. If the length of the slider is

L

, the total effective length over which the surface tension acts is

2 L

Therefore, the total upward force due to surface tension is:

F_{S} = S \times (2 L)

The Balancing Act

For the slider to remain stationary, the upward force must perfectly balance the downward force.

F_{upward} = F_{downward}

S \times (2 L) = W

We can rearrange this equation to solve for the surface tension

S

S = \frac{W}{2 L}

The Final Calculation

Now, it's just a matter of plugging in the numbers. We are given the weight

W = 1.5 \times 1 0^{- 2} N

and the length of the slider

L = 30 cm = 0.3 m

S = \frac{1.5 \times 1 0 ^{- 2}}{2 \times 0.3}

S = \frac{1.5 \times 1 0 ^{- 2}}{0.6}

S = 2.5 \times 1 0^{- 2} N/m

Converting this to a decimal, we get:

S = 0.025 N/m

The surface tension of the liquid film is

0.025 N/m

, which corresponds to option (d).

Common Traps & FAQs

Why do we multiply the length by 2?

A soap or liquid film has two surfaces (front and back). Both surfaces exert a surface tension force on the slider, so the effective length is

2 L

What if it was a liquid surface instead of a film?

If it were a single surface (like a slider resting on top of a water bath), we would only use

L

because there is only one surface in contact.

Does the weight of the slider matter?

The problem states the slider is 'light' or has 'negligible weight'. If it had mass, we would have to add its weight to

W

to find the total downward force.

Why is the unit of surface tension N/m?

Surface tension is defined as the force exerted per unit length of the boundary. Hence, Force (N) divided by Length (m) gives N/m.

What happens if the weight is slightly increased?

The slider would move downwards, stretching the film until it breaks, because the surface tension force has a maximum limit based on the film's properties.

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* Multiple Correct Options

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A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $σ$ . The angle of contact between water and the wall of the capillary tube is $θ$ . Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

* Multiple Correct Options

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(D)

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Select Answer:

Visualized Solution

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The Sigma Insight: Surface Tension and Capillary Action

The Setup

The Hidden Trap

The Balancing Act

The Final Calculation

Similar Questions

Visualizing the Setup

Equilibrium Condition

Surface Tension Force

Formulating the Equation

Substituting Values

Simplifying Denominator

Final Answer