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Question:

A bottle has an opening of radius a and length b. A cork of length b and radius (a+Δa), where (Δa<<a), is compressed to fit into the opening completely. If the bulk modulus of cork is B and the frictional coefficient between the bottle and cork is μ, then the force needed to push the cork into the bottle is:

(2πμBb)Δa

(4πμBb)Δa

(πμBb)a

(πμBb)Δa

Solution:

P=NA=N(2πa)b⇒Stress =B×strain
N(2πa)b=B2πaΔa×b
πa2bf=μN=μ4πbΔaB