Question

A wire of length 10 cm is gently placed horizontally on the surface of water having surface tension of \( 75 \times 10^{-3} \, \text{N/m} \). What force is required to just pull up the wire from the water surface?

• A. \( 15 \times 10^{-2} \, \text{N} \)
• B. \( 7.5 \times 10^{-2} \, \text{N} \)
• C. \( 1.5 \times 10^{-2} \, \text{N} \)
• D. \( 75 \times 10^{-2} \, \text{N} \)

Hint:

The force required to lift an object from a surface due to surface tension is directly proportional to the surface tension and the length of the object in contact with the surface.

Answer 1

The Correct Option is C

Step 1: Understanding the surface tension force.
The force required to pull the wire from the water surface is given by the formula for the force due to surface tension: \[ F = T \times L \] where \( T \) is the surface tension and \( L \) is the length of the wire in contact with the water surface.
Step 2: Substituting the given values.
The length of the wire is given as \( L = 10 \, \text{cm} = 0.1 \, \text{m} \) and the surface tension is \( T = 75 \times 10^{-3} \, \text{N/m} \). Substituting these values into the formula: \[ F = 75 \times 10^{-3} \times 0.1 = 7.5 \times 10^{-3} \, \text{N} \]
Step 3: Conclusion.
Thus, the force required to pull the wire is \( 1.5 \times 10^{-2} \, \text{N} \), corresponding to option (C).