A bottle has an opening of radius $a$ and length $b$. A cork of length band radius $\left( {a + \Delta a} \right)$ where $\left( {\Delta a < < a} \right)$ 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 $\mu $ then the force needed to push the cork into the bottle is
JEE MAIN 2016, Diffcult
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