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]
- = 51 (2 - 451 )/
- = 51 (2 - 251 )/3
- = 51 (2 - 451 )/3
- = 51 (2 - 251 )/
Answer
(3) = 51 (2 - 451 )/3
Solution
Rolling without slipping on a fixed disk: centre speed = r, and the centre moves on a circle of radius R + r = 51r.
Angular speed of centres about O: 1 = r51r = 51, 2 = 2 51; they move apart, so relative angular speed = 3 51.
Initial contact: 2r = (R+r) = 251.
To touch again from the other side, the angular gap to be covered = 2 - 2 = 2 - 451.
= 2 - 4513 /51 = 51 (2 - 451 )/3
Answer: (C)