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Chapter 7: Problem 981

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) \(10 \mathrm{TL}\)

Short Answer

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

Step by step solution

01

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 \(4L\).
02

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 \(2*4L = 8L\).
03

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 \(F = T \times (8L)\).
04

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) \(8 \mathrm{TL}\).

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