A uniform solid hemisphere A of mass M radius R is joined with a thin uniform hemispherical shell B of mass M and radius R (see fig.). The sphere thus formed is placed inside a fixed box as shown. The floor , as well as walls of the box are smooth. On slight disturbance, the sphere begins to rotate. Find its maximum angular speed `(omega)` and maximum angular acceleration `(alpha_(0))` during the subsequent motion. Do the walls of the box apply any force on the sphere while it rotates ?

Answer

`omega_(0) = sqrt((15)/(32) (g)/(R)) ; alpha_(0) = (15)/(128) (g)/(R)`; yes