A very thin circular wire ring of mean radius R is slowly pulled vertically upward from a perfectly wetting liquid of surface tension S. Neglect the weight of the ring and buoyancy at the instant of detachment. What minimum upward force is required to detach the ring?
Options

Question

A very thin circular wire ring of mean radius R is slowly pulled vertically upward from a perfectly wetting liquid of surface tension S. Neglect the weight of the ring and buoyancy at the instant of detachment. What minimum upward force is required to detach the ring?

Options

G1 Physics · Accepted Answer

For a thin circular ring, the liquid is in contact with both the inner and outer circumferences. Inner contact length: L₁ = 2πR. Outer contact length: L₂ = 2πR. Therefore the total effective contact length is L = L₁+L₂ = 4πR. For perfect wetting, the vertical surface-tension force is F = SL. Hence, F = S(4πR) = 4πRS. Correct option: B.