Problem 981 - JEE Physics

Question

A square frame of side \(\mathrm{L}\) is dipped in a liquid on taking out a membrance is formed if the surface tension of the liquid is \(\mathrm{T}\), the force acting on the frame will be. (A) \(2 \mathrm{TL}\) (B) \(4 \mathrm{TL}\) (C) \(8 \mathrm{TL}\) (D) \(10 \mathrm{TL}\)

Step-by-Step Solution

Answer

The total force acting on the square frame after being dipped in a liquid is (C) \(8 \mathrm{TL}\).

Step 1: Total length of the frame

Firstly, note that this frame is a square, so it has four sides of equal length, L. We can calculate the total length around the frame, which is \(4L\).

Step 2: Total number of surfaces contributing to the force

We know that when the frame is pulled out of the liquid, layer of liquid forms on both surfaces (the top and bottom), we realize that we need to multiply the length from step 1 by 2, because each side of the length is associated with two sides of liquid (one on top, and one on the bottom). Therefore, the total contributing length is \(2*4L = 8L\).

Step 3: Apply the definition of surface tension

To find the force we apply the definition of surface tension, which is the force acting per unit length. So, by knowing surface tension (T) and the total contributing length, we get the total force by multiplying the surface tension by the total length, or \(F = T \times (8L)\).

Step 4: Identifying the correct choice

By comparing our result from Step 3 with the provided choices in the multiple choice question, we see that the answer to the problem is (C) \(8 \mathrm{TL}\).

Key Concepts

Force Calculation

Understanding force calculation in the context of surface tension involves recognizing how different surfaces contribute. Surface tension, denoted by \( T \), is essentially the force exerted along the surface of the liquid per unit length.
For this problem, it’s about determining the total force exerted on a square frame covered with a liquid film. If we calculate the total length of the frame with liquid (

• The frame has four sides, making the total frame length \( 4L \).
• Each side interacts with two layers of liquid film – one on each side – so the total length becomes \( 8L \).

The force exerted by surface tension would thus be \( F = T \times 8L \). This results in the force calculated as \( 8TL \), matching the correct answer from the choices given.

Square Frame

The square frame is an integral part of understanding the force calculation problem. A square consists of four equal sides, each of length \( L \).
This geometric property ensures that any calculation concerning the frame must consider the entire perimeter, which is \( 4L \).
The uniformity of the square makes it a straightforward case for calculating interactions with surface tension.

• Every side of the square plays an equal role in contact with the liquid.
• This symmetry simplifies how the force is distributed across the frame.

Thus, when dealing with a square frame immersed in a liquid, always remember the total interaction length isn't just the perimeter, but it involves two surfaces.

Liquid Membrane

In this context, the liquid membrane formed has a significant influence on the force experienced by the frame. When the frame is pulled out, a thin layer of liquid sticks to it, forming what we call a membrane.
This membrane exists on both sides of the frame, which is crucial for force calculations. Each side of the square frame is covered by two layers:

• One layer on the top of the frame.
• Another layer beneath the frame.

These dual layers mean that the interactions happen twice over every length of the frame, doubling the effect of the surface tension forces. This is why the multiplication factor of two is used when calculating the total length that influences the force on the frame.

Physics Problem Solving

Solving physics problems, like this one involving surface tension, involves a step-by-step logical approach. Start by understanding the problem statement, and identify all given data.
Then, use these steps to systematically find a solution:

• Break down calculations into smaller, manageable parts, like calculating the perimeter for the square frame.
• Consider all contributing factors, such as the dual layers of the liquid membrane.
• Apply relevant formulas, like those for surface tension, smoothly integrating them into your calculations.

Finally, compare your answer with the given choices to ensure its correctness. This problem-solving method helps simplify complex problems into easy-to-understand steps, enhancing comprehension and ensuring accuracy.