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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 N m⁻¹, then the excess force required to take it away from the surface is:
A flat disc touches liquid along its single outer boundary (L = 2πR) -> F = T × 2πR = 0.07 × 2π(0.045) = 19.8 mN!
When a flat solid circular disc of radius R rests on the surface of water, the water film clings to the boundary circumference of the disc. The perimeter along which the surface tension acts downwards as the disc is pulled upward is:
Surface tension T is force per unit length. The additional upward force F needed to overcome surface tension and detach the disc is:
Substitute T = 0.07 N m⁻¹ and R = 4.5 cm = 0.045 m:
Using π ≈ 3.1416:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Off by a factor of 10.
Extreme magnitude error.
Accurate surface tension force: F = 2πRT = 19.8 mN.
Off by four orders of magnitude.
Students frequently use L = 4πR (the formula for an annular ring with both inner and outer circumferences) for a solid disc.
"The force due to surface tension is F = T · L, where L is the total contact perimeter."
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