Top pipe falls

There is a system consisting of 3 pipes(hollow cylinders as shown in the figure). Now, the system is little disturbed. Let the initial downward acceleration of the top pipe given the conditions be

\(a_1\) - When there is friction between the 2 cylinders and the ground but there is no friction between any of the pipes.

\(a_2\) - When there is no friction between the 2 cylinders and the ground but there is friction between the pipes.

Find \(\displaystyle \frac{a_1}{a_2}\).

If your answer is of the form \(\frac{p}{q}\)(for co-prime \(p,q\)), give your answer as \(p+q\)

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