Rotational Dynamics

Three identical blocks of length L are stacked together as shown. The blocks 2 and 3 are slided towards the right.
Figure shows a smooth fixed track with two straight parts connected by a semicircular arc $$ABC$$. The shown track is placed in a vertical plane. A small ball is given an initial speed $$u$$ along the track somewhere in the part $$BC$$ and collides with the track at $$A$$ during subsequent motion. Now answer the following questions
The figure shows an isosceles triangular plate of mass M and base L. The angle at the apex is $$90^o$$. The apex lies at the origin and the base is parallel to X-axis.
A solid body rotates with angular velocity $$\omega=at\hat{i}+bt^2\hat{j}$$, where $$a=0.50\:rad/s^2$$, $$b=0.060\:rad/s^3$$, and $$\hat{i}$$ and $$\hat{j}$$ are the unit vectors of the x and y axes.
A light thread with a body of mass $$m$$ tied to its end is wound on a uniform solid cylinder of mass $$M$$ and radius $$R$$ (figure shown above). At a moment $$t=0$$ the system is set in motion.