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Question: A soap film of surface tension \(3\times {{10}^{-2}}\) formed in a rectangular frame can support a s...

A soap film of surface tension 3×10−23\times {{10}^{-2}} formed in a rectangular frame can support a straw as shown in the figure. If g=10ms−2g=10m{{s}^{-2}}, the mass of the straw is:

A. 0.006g
B. 0.06g
C. 0.6g
D. 6g

Explanation

Solution

Hint: This question needs the knowledge of surface tension to solve this problem. Good understanding of how the forces are acting on the straw will help in solving this question. The surface tension formula is:T=FSTlT=\dfrac{{{F}_{ST}}}{l}.

Step by step solution:
Let’s start by understanding what is surface tension after all. As the word suggests, it is linked to a surface of the liquid. The surface tension is a physical property of the liquids only, which happens when the molecules from all the sides are drawn closer. This inward attracting force by all the molecules is known as the surface tension, which is given by the dragging force per unit length. That is the surface tension (T) is, T=FSTlT=\dfrac{{{F}_{ST}}}{l}.

In the current problem, the straw of mass m is supported by the soap film. The straw due to its mass and no other force acting on it, has only a single force acting on it, which is due to gravity.

Hence, the downward force acting on the straw is mg. The upward force acting against the downward force of the straw is the force due to the surface tension. The force due to surface tension is given by, FST=Tl{{F}_{ST}}=Tl. Here, l is the length of the straw, upon which the surface tension is acting. Here, since a soap film is used, hence the surface tension becomes, FST=2Tl{{F}_{ST}}=2Tl.

Hence, equating both the downwards force and upwards force to be equal, we get, mg=2Tlmg=2Tl.

Putting in the value of g=10ms−2g=10m{{s}^{-2}}, T=3×10−2Nm−13\times {{10}^{-2}}N{{m}^{-1}} and l=10cm=10×10−2m10\times {{10}^{-2}}minto this equation, we get, m(10)=2(3×10−2)(10×10−2)kg⇒m=6×10−4kg⇒m=6×10−1gm(10)=2(3\times {{10}^{-2}})(10\times {{10}^{-2}})kg\Rightarrow m=6\times {{10}^{-4}}kg\Rightarrow m=6\times {{10}^{-1}}g.
Therefore the mass of the straw is equal to 0.6g.

Note:It’s important to know that the force of the surface tension supporting the mass of the straw by the soap film is twice the surface tension, because two surfaces contribute to the force. The two surfaces being the upper and the lower half of the whole film.
For better visualization, if you consider the film to be a sphere, the two surfaces would be the two hemispheres.