A thread is tightly wrapped on two pulleys as shown in figure. Both the pulleys are uniform disc with upper one having mass M and radius R being free to rotate about its central horizontal axis. The lower pulley has mass m and radius r and it is released from rest. It spins and falls down. At the instant of release a small mark (A) was at the top point of the lower pulley.
(a) After what minimum time `(t_(0))` the mark will again be at the top of the lower pulley?
(b) Find acceleration of the mark at time `t_(0)`.
(c) Is there any difference in magnitude of acceleration of the mark and that of a point located on the circumference at diametrically opposite end of the pulley.

Answer

(a) `t_(0) = sqrt((2pi (2m + 3M)r)/(Mg))`
(b) `a = (2g)/(2m + 3M)n sqrt(m^(2) + (4 pi M + M + m)^(2))`
(c) yes