A thin horizontal annular plate of outer radius R and inner radius r is slowly withdrawn from a perfectly wetting liquid of surface tension S. At the instant of detachment, assume the vertical component of surface tension acts along the complete outer and inner boundaries. Neglect the weight of the plate. What is the total surface-tension force?
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Question

A thin horizontal annular plate of outer radius R and inner radius r is slowly withdrawn from a perfectly wetting liquid of surface tension S. At the instant of detachment, assume the vertical component of surface tension acts along the complete outer and inner boundaries. Neglect the weight of the plate. What is the total surface-tension force?

Options

G1 Physics · Accepted Answer

The surface-tension force is proportional to the total length of the contact line. Outer perimeter: L(outer) = 2πR. Inner perimeter: L(inner) = 2πr. Therefore, L(total) = 2π(R+r). For perfect wetting, the vertical surface-tension force is F = S L(total). Hence, F = 2πS(R+r). Correct option: B.