In the arrangement shown, the double pulley has a mass M and the two mass less threads have been tightly wound on the inner (radius `= r`) and outer circumference (radius `R = 2r`). The block shown has a mass 4 M. The moment of inertia of the double pulley system about a horizontal axis passing through its centre and perpendicular to the plane of the figure is `I = (Mr^(2))/(2)`.
(a) Find the acceleration of the center of the pulley after the system is released.
(b) Two seconds after the start of the motion the string holding the block breaks. How long after this the pulley will stop ascending?

Answer

(a) `(6g)/(11)`
(b) `(18)/(11)s`