System of Particles and Rotational Motion

Consider a large disk of radius R and two smaller disks, each of radius r = R/50, lying on its circumference, as shown in the figure. The smaller disks are initially in contact with each other, with an angular separation between their centers. They are made to roll without slipping in opposite directions, with constant angular velocities and 2 while the large disk is held stationary. The time at which the smaller disks are again in contact is: [Use ( ) = and ignore gravity.] [figure]

1. = 51 (2 - 451 )/
2. = 51 (2 - 251 )/3
3. = 51 (2 - 451 )/3
4. = 51 (2 - 251 )/

A solid cylinder of radius R rolls without slipping with a center of mass speed v0 = gR3 on a horizontal surface with a vertical edge, as shown in the figure. Here, g is the acceleration due to the gravity. At the moment when the cylinder loses contact with the surface due to rotation around the corner, the speed of its center of mass is: [figure]

1. 0
2. 5gR7
3. gR15
4. 3gR7