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Question: A 10 cm long wire is placed horizontally on the surface of water and is gently pulled up with a forc...

A 10 cm long wire is placed horizontally on the surface of water and is gently pulled up with a force of 2×10−2N2\times {{10}^{-2}}N. To keep the wire in equilibrium, the surface tension of water in Nm−1N{{m}^{-1}} is.
A. 0.1
B. 0.2
C. 0.001
D. 0.002

Explanation

Solution

Hint: Here we have already given the force that we are applying and the length of the wire. For an equilibrium motion, the force per unit length has to be equal to the surface tension. So we can find the surface tension of the liquid from the given information.

Formula used:
S=FdS=\dfrac{F}{d}, where F is the force and d represents the length along which the force felt.

Complete step by step answer:
Surface tension is an attractive force in liquids to minimise the surface area. This is mainly due to the attraction between the surface molecules and the rest of the liquid molecules. The general formula of surface tension can be written as,
S=FdS=\dfrac{F}{d}, where F is the force and d represents the length along which the force felt.
We are going to place a wire on the surface of the liquid and gently pull it up. To keep it in equilibrium, the product of force per unit length has to be equal to the intermolecular forces that are causing the surface tension.
Since there are two surfaces on the liquid film, we have to multiply the length by two.
F=2d×SF=2d\times S
We can use the given information in the question. Force on the water is 2×10−2N2\times {{10}^{-2}}N and the length of the wire is 10 cm.
S=2×10−22×10×10−2S=\dfrac{2\times {{10}^{-2}}}{2\times 10\times {{10}^{-2}}}
S=0.1Nm−1S=0.1N{{m}^{-1}}
Therefore, the correct option is A.

Note: The molecules at the surface do not have any other forces except from the molecules that are situating below to the surface layer. These surface molecules are attracted by the rest of the liquid. This will result in a surface film, which makes the movement difficult to any object through the surface. Because of this film behaviour, we have to consider two surfaces for the film. That’s why we are multiplying the length by two. In bubbles also, we have to consider two surfaces.