A disc rotates freely with rotational kinetic energy E about a normal axis through centre. A ring having the same radius but double the mass of disc is now. gently placed on the disc. the new rotational kinetic energy of the system would be

A horizontal disc rotates freely with angular velocity omega about a vertical axes through its centre. A ring having the same mass and radius as the disc, is now gently placed coaxially on the disc. After some time, the two rotate with a common angular velocity. then.

Two identical discs are positioned on a vertical axis as shown in the figure. The bottom disc is rotating at angular velocity omega_(0) and has rotational kinetic energy K_(0) .The top disc is initially at rest. It then falls and sticks to the bottom disc. The change in the rotational kinetic energy of the system is

The rotational kinetic energy of a body is E. In the absence of external torque, the mass of the body is halved and its radius of gyration is doubled. Its rotational kinetic energy is

A solid cylinder of mass M and radius R rotates about its axis with angular speed omega . Its rotational kinetic energy is

A quarter disc of radius R and mass m is rotating about the axis OO' (perpendicular to the plane of the disc) as shown. Rotational kinetic energy of the quarter disc is

A uniform disc of radius a and mass m, is rotating freely with angular speed omega in a horizontal plane about a smooth fixed vertical axis through its centre. A particle, also of mass m, is suddenly attached to the rim of the disc of the disc and rotates with it. The new angular speed is

A thin circular metal disc of radius 500.0 mm is set rotating about a central axis normal to its plane. Upon raising its temperature gradually, the radius increases to 507.5 mm. The percentage change in the rotational kinetic energy will be

A thin circular metal disc of radius 500.0 mm is set rotating about a central axis normal to its plane. Upon raising its temperature gradually, the radius increases to 507.5 mm. The percentage change in the rotational kinetic energy will be

A uniform rod of mass m and length L lies radialy on a disc rotating with angular speed omega in a horizontal plane about vertical axis passing thorugh centre of disc. The rod does not slip on the disc and the centre of the rod is at a distance 2L from the centre of the disc. them the kinetic energy of the rod is

A circular disc rolls down an inclined plane . The ratio of rotational kinetic energy to total kinetic energy is