Question

A thin wire is bent in the form of a ring of diameter 3 cm. The ring is placed horizontally on the surface of soap solution and then raised up slowly. How much upward force is necessary to break the vertical film formed between the ring and the solution? (Given that surface tension of soap solution is 0.05N/m)
A) 5.452×10^-3 N
B) 4.452×10^-3 N
C) 6.452×10^-3 N
D) 9.452×10^-3 N

Answer 1

Hint: When we place a ring on the surface of any liquid, surface tension will be created between the surface of liquid and the circular wire. Some amount of force to be applied to break the surface created. As per the question here we have to find out the amount of force required to break the surface tension created between the soap solution and the circular wire.

Complete step by step solution:
A thin wire has bent as a circular ring and kept horizontally on the soap solution. When we keep it on a surface of soap solution a thin film is formed due to surface tension. Surface tension force at the top layer and at the bottom layer of the wire. Here, we have to find the force required to break the surface tension.
First, we write all the given data in the question.
Diameter of the ring of wire, d = 3 cm = 0.03 m (converted from cm to m)
The wire has bent in a circular ring. Diameter of a circle is always half of the radius of the circle. Now, we easily find the radius.
Radius of ring of wire r = half of the diameter = $0.03 \times {\dfrac12}$ m=0.015m
Surface tension of soap solution, k = 0.05 N/m
The length of the ring will be equal to circumference of circle =2πr=2×3.14×0.015
                                                                                                               =0.0942m
Now, we have to find out the surface tension on this particular region.
The general formula for measuring surface tension is equal to force divided by length.
Surface tension, k=$\dfrac{F}{L}$
The upward force is given as F=kL
We have to apply an upward force which is 2 times the surface tension.
Hence F=2kL
Now, we can substitute the values of length and surface tension in the above equation.
F=2×0.05×0.0942
F=9.42×10^-3 N
Hence the correct answer is option D.

Note: Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. Surface tension allows insects, usually denser than water, to float and slide on a water surface.