Question

The length of a needle floating on water is 2.5 centimeters. The minimum force in addition to the ties weight needed to lift the needle above the surface of the water will be (surface tension of the water is 0.072 N/m)
A.)$3.6 \times 10^{-3} N$
B.)$10^{-2} N$
C.)$9 \times 10^{-4} N$
D.)$6 \times 10^{-4} N$

Answer 1

Hint: The surface tension is the force acting per unit length on the surface molecules due to the bulk present below the surface of the liquid. So we can calculate the force of acting on the total length of the needle using the surface tension and the length of the needle and when we can determine the force required to pull up the needle.

Step by step solution:
To solve the problem we need to understand the concept of surface tension. The surface tension is nothing but the force acting per unit length of the body on the surface of the water or liquid. So we can define the mathematical expression for the surface tension as:

$T = \dfrac{F}{L}$
Now we are given the value of the length of the needle as: 2.5 cm = $2.5 \times 10^{-2} m$
We are given the surface tension of the liquid as: $\dfrac{F}{L} = 0.072 \dfrac{N}{m}$
The effective length of the needle will be 2 times its length so we get L = $2 \times 2.5 = 5$ cm

So we can now use the formula for the surface tension of the liquid and we can substitute the given values to get the force acting on the needle as:

$F = L \times T = 0.072 \times 5 \times 10^{-2} = 3.6 \times 10^{-3} N$
Hence the value of the force acting on the given needle becomes: $3.6 \times 10^{-3} N$

Additional information:
The surface tension is due to the force applied by the bulk of the molecules present below the surface of the liquid and we call the force applied per unit length of the surface has the surface tension of the liquid. For the viscous liquid surface tension is more and hence we need greater force to remove the needle.

Note:
There is a common misconception that the surface tension is nothing but the force acting on the surface of the water for any liquid which is wrong. The surface tension is defined as the force per unit length of the surface of the liquid. We need to take care of this while solving the problem so that we can get the required force to get the needle on the surface of the water.