Viscosity + Rotation combined

A cylindrical container of radius R has a cylindrical lid, with liquid filled up to height h. The fluid has a coefficient of viscosity

. The lid has mass M and is rotated with angular velocity
in clockwise sense as seen from top. At the same time a force F acts at a distance R/2 opposing the angular velocity.

Find the time after which the lid comes momentarily to rest.

If the answer is of form

find a+b+c

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