A unique rope and pulley problem

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A uniform heavy rope of length 2l is positioned over a smooth pulley, with the right side measuring (l+a) and the left side (l-a). The discussion focuses on determining the time it takes for the shorter portion of the rope to slip off the pulley after being released. Participants are encouraged to provide their solutions and reasoning. Additionally, newcomers are reminded to adhere to forum guidelines by posting in the appropriate section and demonstrating effort in their inquiries. Engaging with the community effectively can lead to better assistance.
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A uniform heavy rope of length 2l goes over a small smooth pulley such that the right end has length (l+a) while the left end has length (l-a). The shorter portion is held and then released. Find the time taken for the rope to slip off the pulley.
 
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