A ring of mass `m` and radius `r` rotates about an axis passing through its centre and perpendicular to its plane with angular velocity `omega`. Its kinetic energy is

Radius of gyration of a ring of radius R about an axis passing through its centre and perpendicular to its plane is

A disc of mass 2 kg and radius 0.2 m is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity 50 rad/s. Another disc of mass 4 kg and radius 0.1m rotates about an axis passing through its centre and perpendicular to its plane with angular velocity 100 rad/s. If the two discs are coaxially coupled, then the angular velocity of the coupled system would be

A disc of mass 2 kg and radius 0.2 m is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity 50 rad/s . Another disc of mass 4 kg and radius 0.1m rotates about an axis passing through its centre and perpendicular to its plane with angular velocity 100 rad/s. If the two disc are coaxially coupled, then the angular velocity of coupled system would be

A thinuniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane withan angular velocity omega .Another disc of same dimensions but of mass M/4 is placed gently onthe first disc co-axially, then the angular velocity of the system is

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to the plane with angular velocity omega . Another disc of same mass but half the radius is gently placed over it coaxially. The angular speed ofthe composite disc will be:

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity omega . Another disc of same dimensions but of mass (1)/(4) M is placed gently on the first disc co-axially. The angular velocity of the system is

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity omega . Another disc of same dimensions but of mass (1)/(4) M is placed gently on the first disc co-axially. The angular velocity of the system is