Question

There is a horizontal film of soap solution. A thread is placed on it, in the form of a loop. The film inside the loop is punctured and the thread becomes a circular loop of radius R. If the surface tension of the soap solution be T, then the tension in the thread will be,

Open in App

Solution

The correct option is **C** 2RT

Consider a very small portion of film, approximately similar to a straight part. Now, the forces on it are as shown below.

F denotes the tension in the thread and T denotes the surface tension.

∴F=2T×d, is the force due to surface tension, since there are two free surfaces.

So, 2F sin dθ=2T×[2×R(dθ)]

we get sin(dθ)≈dθ, for small value of dθ

The net force acting on the bubble is,

2Fdθ=4TRdθ⇒ F=2TR

Hence, (C) is the correct answer.

Consider a very small portion of film, approximately similar to a straight part. Now, the forces on it are as shown below.

F denotes the tension in the thread and T denotes the surface tension.

∴F=2T×d, is the force due to surface tension, since there are two free surfaces.

So, 2F sin dθ=2T×[2×R(dθ)]

we get sin(dθ)≈dθ, for small value of dθ

The net force acting on the bubble is,

2Fdθ=4TRdθ⇒ F=2TR

Hence, (C) is the correct answer.

1

View More