Two coaxial solenoids are made by winding their insulated wire over a pipe of cross sectional area $A= 10\;cm^2$ length $20\;cm$ .One of the solenoids has 200 turns and another 400 turns. the mutual inductance is .

Question

$(a)\;2.4 \times 10^{-4} \pi H \\(b)\;2 \times 10^{-4} \; \pi H \\ (c)\;1.6 \times 10^{-4} \;\pi \;H \\ (d)\;8 \times 10^{-4} \; \pi H $