A bottle has an opening of radius a and length b. A cork of length b and radius (a+a) where (a<<a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is µ then the force needed to push the cork into the bottle is :
(πµB b) a
(2πµB b) a
(πµB b) a
(4πµB b) a