A horizontal disc of radius R and mas 20 M is pivoted to rotate freely about a vertical axis through its centre. A small insect A of mass M and another small insect B of mass `m (M)/(4)` are initially at diametrically opposite points on the periphery of the disc. The whole system is imparted an angular speed `omega_(0)` Insect A walks along the diameter with constant velocity v relative to the disc unit it reaches B which remains at rest on the disc. A then eats B and returns to its starting point along the original path with same speed v relative to the disc.
(a) Find the angular speed of the disc when A reaches the centre after eating B.
(b) Plot approximately, the variation of angular speed of the disc with time for the entire journey of the insect A.
