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: Use the Formula for Force Due to Surface Tension

The force required to overcome surface tension is given by:

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

Where:

$F$ = Force due to surface tension

$r$ = Radius of the liquid surface

$T$ = Surface tension

Step 2: Convert Radius to Meters

Given:

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

Step 3: Substitute the Values

Given surface tension:

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

Substituting the values into the formula:

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

Step 4: Solve for $F$

Calculating:

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

Converting to milliNewtons:

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

Conclusion

The force required to overcome surface tension is 19.8 mN.