A hollow cylindrical pipe A has mass M and radius R. With the help of two identical springs (each of force constant k) it is connected to solid cylinder B having mass M and radius R. The springs are connected symmetrically to the axle of the cylinders. Moment of inertia of the two Bodies A and B about their axles are `I_(A) = MR^(2)` and `I_(B) = (1)/(2) MR^(2)` respectively. Cylinders are pulled apart so as to stretch the springs by x0 and released. During subsequent motion the cylinders do not slip.
(a) Find acceleration of the centre of mass of the system immediately after it is released.
(b) Find the distance travelled by cylinder A by the time it comes to rest for the first time after being released.

Answer

(a) `(kx_(0))/(6M)`
(b) (6x_(0))/(7)`