please solve this problem:

7. 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 $\mu$ then the force needed to push the cork into the bottle is:

$$\begin{gathered} \left(1\right) \left(\mathrm{\pi \mu B} \mathrm{b}\right) △\alpha \\ \left(2\right) \left(2\mathrm{\pi \mu B} \mathrm{b}\right) △\alpha \\ \left(3\right) \left(\mathrm{\pi \mu B} \mathrm{b}\right) \alpha \\ \left(4\right) \left(4\mathrm{\pi \mu B} \mathrm{b}\right) △\alpha \end{gathered}$$