System of Particles and Rotational Motion · Question 8

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

List-I shows four planar structures made of uniform solid rods each of mass m and length l. In the List-II the possible moment of inertia of these structures about an axis OCO', which lies in the plane of the structures, are given. Choose the option that describes the correct match between the entries in List-I to those in List-II.

1. P→5, Q→1, R→4, S→2
2. P→1, Q→3, R→4, S→2
3. P→5, Q→3, R→2, S→1
4. P→5, Q→4, R→2, S→1

After the collision the disk starts to rotate around point C in the XY plane. The maximum change in the height (in m) of its center O is:

Amount of energy loss (in J) in the collision is:

A disc of mass M and radius R is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass M and radius R/2 is fixed to the motor's thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed . If the angular speed at which the large disc rotates is /n, then the value of n is . [figure]

A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x=L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is . [figure]