Question

A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 Nm^-1, then the excess force required to take it away from the surface is :

• A. 19.8 mN
• B. 198 N
• C. 1.98 mN
• D. 99 N

Answer 1

The Correct Option is A

Step 1: Calculate Force Due to Surface Tension

The formula for the force needed to overcome surface tension is:

$$ F = 2\pi r \cdot T $$

Where:

\( F \) = Force from surface tension

\( r \) = Radius of the liquid surface

\( T \) = Surface tension value

Step 2: Convert Radius to Meters

Given radius:

$$ r = 4.5 \text{ cm} = 0.045 \text{ m} $$

Step 3: Input Values into Formula

Given surface tension:

$$ T = 0.07 \text{ N/m} $$

Substitute values:

$$ F = 2\pi (0.045) (0.07) $$

Step 4: Determine \( F \)

Calculation:

$$ F = 0.0198 \text{ N} $$

Convert to milliNewtons:

$$ F = 19.8 \text{ mN} $$

Final Result

The force required to overcome surface tension is 19.8 mN.