A thin annular plate has outer radius 5 cm and inner radius 2 cm. It is withdrawn vertically from a perfectly wetting liquid of surface tension 0.05 N/m. Neglect the plate weight. If the vertical surface-tension force is Nπ × 10⁻³ N, find N.
Physics · Properties of solid and fluid · properties of fluid and surface tension
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Question

A thin annular plate has outer radius 5 cm and inner radius 2 cm. It is withdrawn vertically from a perfectly wetting liquid of surface tension 0.05 N/m. Neglect the plate weight. If the vertical surface-tension force is Nπ × 10⁻³ N, find N.

Physics · Properties of solid and fluid · properties of fluid and surface tension

G1 Physics · Accepted Answer

The total contact perimeter is L = 2π(R+r). Therefore, F = SL = 2πS(R+r). Substitute S = 0.05 N/m, R = 0.05 m, r = 0.02 m. Then, F = 2π(0.05)(0.07) = 0.007π N = 7π×10⁻³ N. Hence, N = 7.